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# Count of common divisible of two numbers in a range

The given problem is to find the count of common divisible numbers between two given integers `x` and `y` within a given range `[start, last]`. In other words, we need to determine how many numbers in the range are divisible by both `x` and `y`.

## Problem Statement

Given two integers `x` and `y`, and a range `[start, last]`, we need to find and count all the numbers within the range that are divisible by both `x` and `y`.

## Example

Let's take the range from 1 to 50 and consider `x = 4` and `y = 3`.

Step 1: Initialize `counter = 0` to count the divisible numbers. Step 2: Start iterating through the numbers from `start` to `last` (i.e., 1 to 50). Step 3: Check if the current number `num` is divisible by both `x` and `y` using the condition `num % x == 0 && num % y == 0`. Step 4: If the condition is true, increment the `counter` and print the current number. Step 5: Continue the iteration until all the numbers in the given range are checked. Step 6: Display the final count stored in `counter`.

## Pseudocode

``````count_divisible(start, last, x, y):
counter = 0
if start > last:
swap start and last
print "Divisible by (", x, ",", y, ") in range of [", start, "-", last, "] are ["
num = start
while num <= last:
if num % x == 0 && num % y == 0:
print num
counter++
if counter > 0:
if x > y:
num += x
else:
num += y
else:
num++
print "]"
print "Counter :", counter
``````

## Algorithm Explanation

1. The function `count_divisible` takes four parameters: `start`, `last`, `x`, and `y`.
2. We initialize `counter` to 0 to count the divisible numbers between `start` and `last`.
3. If `start` is greater than `last`, we swap their values to ensure that `start` is smaller than or equal to `last`.
4. We start the iteration from `start` to `last`, checking each number in the range.
5. If a number `num` is divisible by both `x` and `y`, we increment the `counter`, print the number, and move to the next number.
6. We use the `counter` value to decide whether to increment `num` by `x` or `y`.
7. If `counter` is greater than 0, we increment `num` by the smaller of `x` and `y`.
8. If `counter` is 0, it means we haven't found any divisible number yet, so we simply increment `num` by 1.
9. After processing all numbers in the range, we print the final count of divisible numbers stored in `counter`.

## Code Solution

Here given code implementation process.

``````// C program
// Count of common divisible of two numbers in a range
#include <stdio.h>

// Count all divisible numbers of x and y in given range
void count_divisible(int start, int last, int x, int y)
{
int counter = 0;
if (start > last)
{
//Change sequence
count_divisible(last, start, x, y);
return;
}
//Display calculated result
printf("\n Divisible by (%d,%d) in range of [%d-%d] are \n  [", x, y, start, last);
int num = start;
while (num <= last)
{
if (num % x == 0 && num % y == 0)
{
printf("  %d", num);
//When x and y are divisible by num
counter++;
}
if (counter > 0)
{
//Increase count value
if (x > y)
{
num += x;
}
else
{
num += y;
}
}
else
{
//When not get first divisible number
num++;
}
}
//Display calculated result
printf(" ]\n Counter : %d\n", counter);
}
int main()
{
//Test case
int x = 4;
int y = 3;
count_divisible(1, 50, x, y);
x = 3;
y = 7;
count_divisible(50, 150, x, y);
x = 2;
y = 5;
count_divisible(1, 100, x, y);
x = 2;
y = 7;
count_divisible(1, 12, x, y);
return 0;
}``````

#### Output

`````` Divisible by (4,3) in range of [1-50] are
[  12  24  36  48 ]
Counter : 4

Divisible by (3,7) in range of [50-150] are
[  63  84  105  126  147 ]
Counter : 5

Divisible by (2,5) in range of [1-100] are
[  10  20  30  40  50  60  70  80  90  100 ]
Counter : 10

Divisible by (2,7) in range of [1-12] are
[ ]
Counter : 0``````
``````/*
Java program
Count of common divisible of two numbers in a range
*/
class Divisor
{
// Count all divisible numbers of x and y in given range
public void count_divisible(int start, int last, int x, int y)
{
int counter = 0;
if (start > last)
{
//Change sequence
count_divisible(last, start, x, y);
return;
}
//Display calculated result
System.out.print("\n Divisible by (" + x + "," + y + ") in range of [" + start + "-" + last + "] are \n [");
int num = start;
while (num <= last)
{
if (num % x == 0 && num % y == 0)
{
System.out.print(" " + num);
//When x and y are divisible by num
counter++;
}
if (counter > 0)
{
//Increase count value
if (x > y)
{
num += x;
}
else
{
num += y;
}
}
else
{
//When not get first divisible number
num++;
}
}
//Display calculated result
System.out.print(" ]\n Counter : " + counter + "\n");
}
public static void main(String[] args)
{
Divisor obj = new Divisor();
//Test case
int x = 4;
int y = 3;
//range (1-50)
obj.count_divisible(1, 50, x, y);
x = 3;
y = 7;
//range (50-150)
obj.count_divisible(50, 150, x, y);
x = 2;
y = 5;
//range (1-100)
obj.count_divisible(1, 100, x, y);
x = 2;
y = 7;
//range (1-12)
obj.count_divisible(1, 12, x, y);
}
}``````

#### Output

`````` Divisible by (4,3) in range of [1-50] are
[ 12 24 36 48 ]
Counter : 4

Divisible by (3,7) in range of [50-150] are
[ 63 84 105 126 147 ]
Counter : 5

Divisible by (2,5) in range of [1-100] are
[ 10 20 30 40 50 60 70 80 90 100 ]
Counter : 10

Divisible by (2,7) in range of [1-12] are
[ ]
Counter : 0``````
``````//Include header file
#include <iostream>
using namespace std;
/*
C++ program
Count of common divisible of two numbers in a range
*/

class Divisor
{
public:
// Count all divisible numbers of x and y in given range
void count_divisible(int start, int last, int x, int y)
{
int counter = 0;
if (start > last)
{
//Change sequence
this->count_divisible(last, start, x, y);
return;
}
//Display calculated result
cout << "\n Divisible by (" << x << "," << y << ") in range of [" << start << "-" << last << "] are \n [";
int num = start;
while (num <= last)
{
if (num % x == 0 && num % y == 0)
{
cout << " " << num;
//When x and y are divisible by num
counter++;
}
if (counter > 0)
{
//Increase count value
if (x > y)
{
num += x;
}
else
{
num += y;
}
}
else
{
//When not get first divisible number
num++;
}
}
//Display calculated result
cout << " ]\n Counter : " << counter << "\n";
}
};
int main()
{
Divisor obj = Divisor();
//Test case
int x = 4;
int y = 3;
//range (1-50)
obj.count_divisible(1, 50, x, y);
x = 3;
y = 7;
//range (50-150)
obj.count_divisible(50, 150, x, y);
x = 2;
y = 5;
//range (1-100)
obj.count_divisible(1, 100, x, y);
x = 2;
y = 7;
//range (1-12)
obj.count_divisible(1, 12, x, y);
return 0;
}``````

#### Output

`````` Divisible by (4,3) in range of [1-50] are
[ 12 24 36 48 ]
Counter : 4

Divisible by (3,7) in range of [50-150] are
[ 63 84 105 126 147 ]
Counter : 5

Divisible by (2,5) in range of [1-100] are
[ 10 20 30 40 50 60 70 80 90 100 ]
Counter : 10

Divisible by (2,7) in range of [1-12] are
[ ]
Counter : 0``````
``````//Include namespace system
using System;

/*
C# program
Count of common divisible of two numbers in a range
*/

class Divisor
{
// Count all divisible numbers of x and y in given range
public void count_divisible(int start, int last, int x, int y)
{
int counter = 0;
if (start > last)
{
//Change sequence
count_divisible(last, start, x, y);
return;
}
//Display calculated result
Console.Write("\n Divisible by (" + x + "," + y + ") in range of [" + start + "-" + last + "] are \n [");
int num = start;
while (num <= last)
{
if (num % x == 0 && num % y == 0)
{
Console.Write(" " + num);
//When x and y are divisible by num
counter++;
}
if (counter > 0)
{
//Increase count value
if (x > y)
{
num += x;
}
else
{
num += y;
}
}
else
{
//When not get first divisible number
num++;
}
}
//Display calculated result
Console.Write(" ]\n Counter : " + counter + "\n");
}
public static void Main(String[] args)
{
Divisor obj = new Divisor();
//Test case
int x = 4;
int y = 3;
//range (1-50)
obj.count_divisible(1, 50, x, y);
x = 3;
y = 7;
//range (50-150)
obj.count_divisible(50, 150, x, y);
x = 2;
y = 5;
//range (1-100)
obj.count_divisible(1, 100, x, y);
x = 2;
y = 7;
//range (1-12)
obj.count_divisible(1, 12, x, y);
}
}``````

#### Output

`````` Divisible by (4,3) in range of [1-50] are
[ 12 24 36 48 ]
Counter : 4

Divisible by (3,7) in range of [50-150] are
[ 63 84 105 126 147 ]
Counter : 5

Divisible by (2,5) in range of [1-100] are
[ 10 20 30 40 50 60 70 80 90 100 ]
Counter : 10

Divisible by (2,7) in range of [1-12] are
[ ]
Counter : 0``````
``````<?php
/*
Php program
Count of common divisible of two numbers in a range
*/
class Divisor
{
// Count all divisible numbers of x and y in given range
public	function count_divisible(\$start, \$last, \$x, \$y)
{
\$counter = 0;
if (\$start > \$last)
{
//Change sequence
\$this->count_divisible(\$last, \$start, \$x, \$y);
return;
}
//Display calculated result
echo "\n Divisible by (". \$x .",". \$y .") in range of [". \$start ."-". \$last ."] are \n [";
\$num = \$start;
while (\$num <= \$last)
{
if (\$num % \$x == 0 && \$num % \$y == 0)
{
echo " ". \$num;
//When x and y are divisible by num
\$counter++;
}
if (\$counter > 0)
{
//Increase count value
if (\$x > \$y)
{
\$num += \$x;
}
else
{
\$num += \$y;
}
}
else
{
//When not get first divisible number
\$num++;
}
}
//Display calculated result
echo " ]\n Counter : ". \$counter ."\n";
}
}

function main()
{
\$obj = new Divisor();
//Test case
\$x = 4;
\$y = 3;
//range (1-50)
\$obj->count_divisible(1, 50, \$x, \$y);
\$x = 3;
\$y = 7;
//range (50-150)
\$obj->count_divisible(50, 150, \$x, \$y);
\$x = 2;
\$y = 5;
//range (1-100)
\$obj->count_divisible(1, 100, \$x, \$y);
\$x = 2;
\$y = 7;
//range (1-12)
\$obj->count_divisible(1, 12, \$x, \$y);
}
main();``````

#### Output

`````` Divisible by (4,3) in range of [1-50] are
[ 12 24 36 48 ]
Counter : 4

Divisible by (3,7) in range of [50-150] are
[ 63 84 105 126 147 ]
Counter : 5

Divisible by (2,5) in range of [1-100] are
[ 10 20 30 40 50 60 70 80 90 100 ]
Counter : 10

Divisible by (2,7) in range of [1-12] are
[ ]
Counter : 0``````
``````/*
Node Js program
Count of common divisible of two numbers in a range
*/
class Divisor
{
// Count all divisible numbers of x and y in given range
count_divisible(start, last, x, y)
{
var counter = 0;
if (start > last)
{
//Change sequence
this.count_divisible(last, start, x, y);
return;
}
//Display calculated result
process.stdout.write("\n Divisible by (" + x + "," + y + ") in range of [" + start + "-" + last + "] are \n [");
var num = start;
while (num <= last)
{
if (num % x == 0 && num % y == 0)
{
process.stdout.write(" " + num);
//When x and y are divisible by num
counter++;
}
if (counter > 0)
{
//Increase count value
if (x > y)
{
num += x;
}
else
{
num += y;
}
}
else
{
//When not get first divisible number
num++;
}
}
//Display calculated result
process.stdout.write(" ]\n Counter : " + counter + "\n");
}
}

function main()
{
var obj = new Divisor();
//Test case
var x = 4;
var y = 3;
//range (1-50)
obj.count_divisible(1, 50, x, y);
x = 3;
y = 7;
//range (50-150)
obj.count_divisible(50, 150, x, y);
x = 2;
y = 5;
//range (1-100)
obj.count_divisible(1, 100, x, y);
x = 2;
y = 7;
//range (1-12)
obj.count_divisible(1, 12, x, y);
}
main();``````

#### Output

`````` Divisible by (4,3) in range of [1-50] are
[ 12 24 36 48 ]
Counter : 4

Divisible by (3,7) in range of [50-150] are
[ 63 84 105 126 147 ]
Counter : 5

Divisible by (2,5) in range of [1-100] are
[ 10 20 30 40 50 60 70 80 90 100 ]
Counter : 10

Divisible by (2,7) in range of [1-12] are
[ ]
Counter : 0``````
``````#   Python 3 program
#   Count of common divisible of two numbers in a range

class Divisor :
#  Count all divisible numbers of x and y in given range
def count_divisible(self, start, last, x, y) :
counter = 0
if (start > last) :
# Change sequence
self.count_divisible(last, start, x, y)
return

# Display calculated result
print("\n Divisible by (", x ,",", y ,") in range of [", start ,"-", last ,"] are \n [", end = "")
num = start
while (num <= last) :
if (num % x == 0 and num % y == 0) :
print(" ", num, end = "")
# When x and y are divisible by num
counter += 1

if (counter > 0) :
# Increase count value
if (x > y) :
num += x
else :
num += y

else :
# When not get first divisible number
num += 1

# Display calculated result
print(" ]\n Counter : ", counter ,"\n", end = "")

def main() :
obj = Divisor()
# Test case
x = 4
y = 3
# range (1-50)
obj.count_divisible(1, 50, x, y)
x = 3
y = 7
# range (50-150)
obj.count_divisible(50, 150, x, y)
x = 2
y = 5
# range (1-100)
obj.count_divisible(1, 100, x, y)
x = 2
y = 7
# range (1-12)
obj.count_divisible(1, 12, x, y)

if __name__ == "__main__": main()``````

#### Output

`````` Divisible by ( 4 , 3 ) in range of [ 1 - 50 ] are
[  12  24  36  48 ]
Counter :  4

Divisible by ( 3 , 7 ) in range of [ 50 - 150 ] are
[  63  84  105  126  147 ]
Counter :  5

Divisible by ( 2 , 5 ) in range of [ 1 - 100 ] are
[  10  20  30  40  50  60  70  80  90  100 ]
Counter :  10

Divisible by ( 2 , 7 ) in range of [ 1 - 12 ] are
[ ]
Counter :  0``````
``````#   Ruby program
#   Count of common divisible of two numbers in a range

class Divisor
#  Count all divisible numbers of x and y in given range
def count_divisible(start, last, x, y)
counter = 0
if (start > last)
# Change sequence
self.count_divisible(last, start, x, y)
return
end

# Display calculated result
print("\n Divisible by (", x ,",", y ,") in range of [", start ,"-", last ,"] are \n [")
num = start
while (num <= last)
if (num % x == 0 && num % y == 0)
print(" ", num)
# When x and y are divisible by num
counter += 1
end

if (counter > 0)
# Increase count value
if (x > y)
num += x
else
num += y
end

else
# When not get first divisible number
num += 1
end

end

# Display calculated result
print(" ]\n Counter : ", counter ,"\n")
end

end

def main()
obj = Divisor.new()
# Test case
x = 4
y = 3
# range (1-50)
obj.count_divisible(1, 50, x, y)
x = 3
y = 7
# range (50-150)
obj.count_divisible(50, 150, x, y)
x = 2
y = 5
# range (1-100)
obj.count_divisible(1, 100, x, y)
x = 2
y = 7
# range (1-12)
obj.count_divisible(1, 12, x, y)
end

main()``````

#### Output

`````` Divisible by (4,3) in range of [1-50] are
[ 12 24 36 48 ]
Counter : 4

Divisible by (3,7) in range of [50-150] are
[ 63 84 105 126 147 ]
Counter : 5

Divisible by (2,5) in range of [1-100] are
[ 10 20 30 40 50 60 70 80 90 100 ]
Counter : 10

Divisible by (2,7) in range of [1-12] are
[ ]
Counter : 0
``````
``````/*
Scala program
Count of common divisible of two numbers in a range
*/
class Divisor
{
// Count all divisible numbers of x and y in given range
def count_divisible(start: Int, last: Int, x: Int, y: Int): Unit = {
var counter: Int = 0;
if (start > last)
{
//Change sequence
count_divisible(last, start, x, y);
return;
}
//Display calculated result
print("\n Divisible by (" + x + "," + y + ") in range of [" + start + "-" + last + "] are \n [");
var num: Int = start;
while (num <= last)
{
if (num % x == 0 && num % y == 0)
{
print(" " + num);
//When x and y are divisible by num
counter += 1;
}
if (counter > 0)
{
//Increase count value
if (x > y)
{
num += x;
}
else
{
num += y;
}
}
else
{
//When not get first divisible number
num += 1;
}
}
//Display calculated result
print(" ]\n Counter : " + counter + "\n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var obj: Divisor = new Divisor();
//Test case
var x: Int = 4;
var y: Int = 3;
//range (1-50)
obj.count_divisible(1, 50, x, y);
x = 3;
y = 7;
//range (50-150)
obj.count_divisible(50, 150, x, y);
x = 2;
y = 5;
//range (1-100)
obj.count_divisible(1, 100, x, y);
x = 2;
y = 7;
//range (1-12)
obj.count_divisible(1, 12, x, y);
}
}``````

#### Output

`````` Divisible by (4,3) in range of [1-50] are
[ 12 24 36 48 ]
Counter : 4

Divisible by (3,7) in range of [50-150] are
[ 63 84 105 126 147 ]
Counter : 5

Divisible by (2,5) in range of [1-100] are
[ 10 20 30 40 50 60 70 80 90 100 ]
Counter : 10

Divisible by (2,7) in range of [1-12] are
[ ]
Counter : 0``````
``````/*
Swift 4 program
Count of common divisible of two numbers in a range
*/
class Divisor
{
// Count all divisible numbers of x and y in given range
func count_divisible(_ start: Int, _ last: Int, _ x: Int, _ y: Int)
{
var counter: Int = 0;
if (start > last)
{
//Change sequence
self.count_divisible(last, start, x, y);
return;
}
//Display calculated result
print("\n Divisible by (", x ,",", y ,") in range of [", start ,"-", last ,"]are \n [", terminator: "");
var num: Int = start;
while (num <= last)
{
if (num % x == 0 && num % y == 0)
{
print(" ", num, terminator: "");
//When x and y are divisible by num
counter += 1;
}
if (counter > 0)
{
//Increase count value
if (x > y)
{
num += x;
}
else
{
num += y;
}
}
else
{
//When not get first divisible number
num += 1;
}
}
//Display calculated result
print(" ]\n Counter : ", counter ,"\n", terminator: "");
}
}
func main()
{
let obj: Divisor = Divisor();
//Test case
var x: Int = 4;
var y: Int = 3;
//range (1-50)
obj.count_divisible(1, 50, x, y);
x = 3;
y = 7;
//range (50-150)
obj.count_divisible(50, 150, x, y);
x = 2;
y = 5;
//range (1-100)
obj.count_divisible(1, 100, x, y);
x = 2;
y = 7;
//range (1-12)
obj.count_divisible(1, 12, x, y);
}
main();``````

#### Output

`````` Divisible by ( 4 , 3 ) in range of [ 1 - 50 ]are
[  12  24  36  48 ]
Counter :  4

Divisible by ( 3 , 7 ) in range of [ 50 - 150 ]are
[  63  84  105  126  147 ]
Counter :  5

Divisible by ( 2 , 5 ) in range of [ 1 - 100 ]are
[  10  20  30  40  50  60  70  80  90  100 ]
Counter :  10

Divisible by ( 2 , 7 ) in range of [ 1 - 12 ]are
[ ]
Counter :  0``````

## Resultant Output Explanation

The provided code is running the function `count_divisible` for four different test cases with different values of `x`, `y`, `start`, and `last`. The output shows the numbers in the given range that are divisible by both `x` and `y`, along with the count of such numbers.

For example, in the first test case with `x = 4` and `y = 3`, the numbers divisible by both 4 and 3 in the range [1-50] are 12, 24, 36, and 48. The total count of such numbers is 4.

## Time Complexity

The time complexity of the provided code is O(N), where N is the number of elements in the given range `[start, last]`. In the worst case, the code will iterate through all the numbers in the given range once. The loop's complexity is directly proportional to the size of the range, so the time complexity is linear.

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