What is the Greatest Common Factor of 17629 and 17646?

Greatest common factor (GCF) of 17629 and 17646 is 17.

GCF(17629,17646) = 17

We will now calculate the prime factors of 17629 and 17646, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17629 and 17646.

How to find the GCF of 17629 and 17646?

We will first find the prime factorization of 17629 and 17646. After we will calculate the factors of 17629 and 17646 and find the biggest common factor number .

Step-1: Prime Factorization of 17629

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

17629 = 17² × 61¹

Step-2: Prime Factorization of 17646

Prime factors of 17646 are 2, 3, 17, 173. Prime factorization of 17646 in exponential form is:

17646 = 2¹ × 3¹ × 17¹ × 173¹

Step-3: Factors of 17629

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

1, 17, 61, 289, 1037

Step-4: Factors of 17646

List of positive integer factors of 17646 that divides 17629 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 173, 346, 519, 1038, 2941, 5882, 8823

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17629 and 17646. The biggest common factor number is the GCF number.
So the greatest common factor 17629 and 17646 is 17.

Also check out the Least Common Multiple of 17629 and 17646