Question

. Let m be a positive integer, find the greatest common divisor of m and m+2

Answer 1

The Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF), or Highest Common Factor (HCF), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.

Let m be a any positive integer.

For example , m=55 and, m+2 =57

factors of 55 are - 1,5 ,11, 55

factors of 57 are -1,3,19,57

Hence the greatest common divisor is 1.

Also,

There are many exceptions such as

For example,m=12 and, m+2=14

Factors of 12 are - 1,2,3,4,6,12

Factors of 14 are -1,2,7,14

Therefore, GCD is 2

There are exceptions but , 1 will be the common divisor for any positive integer (i.e. m and m+2)