What is the Greatest Common Factor of 17612 and 17629?

Greatest common factor (GCF) of 17612 and 17629 is 17.

GCF(17612,17629) = 17

We will now calculate the prime factors of 17612 and 17629, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17612 and 17629.

How to find the GCF of 17612 and 17629?

We will first find the prime factorization of 17612 and 17629. After we will calculate the factors of 17612 and 17629 and find the biggest common factor number .

Step-1: Prime Factorization of 17612

Prime factors of 17612 are 2, 7, 17, 37. Prime factorization of 17612 in exponential form is:

17612 = 2² × 7¹ × 17¹ × 37¹

Step-2: Prime Factorization of 17629

Prime factors of 17629 are 17, 61. Prime factorization of 17629 in exponential form is:

17629 = 17² × 61¹

Step-3: Factors of 17612

List of positive integer factors of 17612 that divides 17612 without a remainder.

1, 2, 4, 7, 14, 17, 28, 34, 37, 68, 74, 119, 148, 238, 259, 476, 518, 629, 1036, 1258, 2516, 4403, 8806

Step-4: Factors of 17629

List of positive integer factors of 17629 that divides 17612 without a remainder.

1, 17, 61, 289, 1037

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17612 and 17629. The biggest common factor number is the GCF number.
So the greatest common factor 17612 and 17629 is 17.

Also check out the Least Common Multiple of 17612 and 17629