What is the Greatest Common Factor of 17605 and 17612?

Greatest common factor (GCF) of 17605 and 17612 is 7.

GCF(17605,17612) = 7

We will now calculate the prime factors of 17605 and 17612, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17605 and 17612.

How to find the GCF of 17605 and 17612?

We will first find the prime factorization of 17605 and 17612. After we will calculate the factors of 17605 and 17612 and find the biggest common factor number .

Step-1: Prime Factorization of 17605

Prime factors of 17605 are 5, 7, 503. Prime factorization of 17605 in exponential form is:

17605 = 5¹ × 7¹ × 503¹

Step-2: 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-3: Factors of 17605

List of positive integer factors of 17605 that divides 17605 without a remainder.

1, 5, 7, 35, 503, 2515, 3521

Step-4: Factors of 17612

List of positive integer factors of 17612 that divides 17605 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17605 and 17612. The biggest common factor number is the GCF number.
So the greatest common factor 17605 and 17612 is 7.

Also check out the Least Common Multiple of 17605 and 17612