The greatest common divisor (gcd), also known as highest common factor (hcf), or greatest common factor (gcf), of two integers a and b is defined as the largest integer that divides both a and b without remainder. The greatest common divisor of two integers a and b is denoted as gcd(a, b).
Example:
Greatest common divisor of 28 and 42:
28 can be expressed as:
28 × 1
2 × 14
4 × 7
Thus the divisors of 28 are: 1, 2, 4, 7, 14, 28
Similarly, 42 can be written as:
42 × 1
21 × 2
14 × 3
7 × 6
Thus the divisors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The divisors that these two numbers have in common are: 1, 2, 7, 14
The greatest of these is 7. So, the greatest common divisor of 28 and 42 is 14, which can be written as gcd(28, 42) = 14
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