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PHP Program to Count Rotations Divisible by 8

Last Updated : 23 Jul, 2025
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Given a large positive number as a string, the task is to count all rotations of the given number which are divisible by 8.

Examples: 

Input : 8
Output : 1

Input : 40
Output : 1
Rotation : 40 is divisible by 8
          04 is not divisible by 8

Input : 13502
Output : 0
No rotation is divisible by 8

Input : 43262488612
Output : 4

Approach

For a large numbers, it is difficult to rotate and divide each number by 8. Therefore, ‘divisibility by 8’ property is used which says that a number is divisible by 8 if the last 3 digits of the number is divisible by 8. Here we do not actually rotate the number and check last 8 digits for divisibility, instead we count consecutive sequence of 3 digits (in circular way) which are divisible by 8.

Illustration  

Consider a number 928160. Its rotations are 928160, 092816, 609281, 160928, 816092, 281609.
Now form consecutive sequence of 3-digits from the original number 928160 as mentioned in the
approach.
3-digit: (9, 2, 8), (2, 8, 1), (8, 1, 6), (1, 6, 0),(6, 0, 9), (0, 9, 2)
We can observe that the 3-digit number formed by the these sets, i.e., 928, 281, 816, 160, 609, 092, are present in the last 3 digits of some rotation.
Thus, checking divisibility of these 3-digit numbers gives the required number of rotations.

PHP 
<?php
// PHP program to count all
// rotations divisible by 8

// function to count of all
// rotations divisible by 8
function countRotationsDivBy8($n) {
    $len = strlen($n);
    $count = 0;

    // For single digit number
    if ($len == 1) {
        $oneDigit = $n[0] - "0";
        if ($oneDigit % 8 == 0) {
            return 1;
        }
        return 0;
    }

    // For two-digit numbers
    // (considering all pairs)
    if ($len == 2) {
      
        // First pair
        $first = ($n[0] - "0") * 10 + ($n[1] - "0");

        // Second pair
        $second = ($n[1] - "0") * 10 + ($n[0] - "0");

        if ($first % 8 == 0) {
            $count++;
        }
        if ($second % 8 == 0) {
            $count++;
        }
        return $count;
    }

    // Considering all three-digit sequences
    $threeDigit;
    for ($i = 0; $i < $len - 2; $i++) {
        $threeDigit = ($n[$i] - "0") * 100 + 
          	($n[$i + 1] - "0") * 10 + ($n[$i + 2] - "0");
        if ($threeDigit % 8 == 0) {
            $count++;
        }
    }

    // Considering the number
    // formed by the last digit
    // and the first two digits
    $threeDigit = ($n[$len - 1] - "0") * 100 + 
      	($n[0] - "0") * 10 + ($n[1] - "0");

    if ($threeDigit % 8 == 0) {
        $count++;
    }

    // Considering the number
    // formed by the last two
    // digits and the first digit
    $threeDigit = ($n[$len - 2] - "0") * 100 + 
      	($n[$len - 1] - "0") * 10 + ($n[0] - "0");
    if ($threeDigit % 8 == 0) {
        $count++;
    }

    // required count
    // of rotations
    return $count;
}

// Driver Code
$n = "43262488612";
echo "Rotations: " . countRotationsDivBy8($n);

?>

Output
Rotations: 4

Time Complexity : O(n), where n is the number of digits in input number.

Auxiliary Space: O(1)

Please refer complete article on Count rotations divisible by 8 for more details!


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