What is the Greatest Common Factor of 19626 and 19635?

Greatest common factor (GCF) of 19626 and 19635 is 3.

GCF(19626,19635) = 3

We will now calculate the prime factors of 19626 and 19635, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19626 and 19635.

How to find the GCF of 19626 and 19635?

We will first find the prime factorization of 19626 and 19635. After we will calculate the factors of 19626 and 19635 and find the biggest common factor number .

Step-1: Prime Factorization of 19626

Prime factors of 19626 are 2, 3, 3271. Prime factorization of 19626 in exponential form is:

19626 = 2¹ × 3¹ × 3271¹

Step-2: Prime Factorization of 19635

Prime factors of 19635 are 3, 5, 7, 11, 17. Prime factorization of 19635 in exponential form is:

19635 = 3¹ × 5¹ × 7¹ × 11¹ × 17¹

Step-3: Factors of 19626

List of positive integer factors of 19626 that divides 19626 without a remainder.

1, 2, 3, 6, 3271, 6542, 9813

Step-4: Factors of 19635

List of positive integer factors of 19635 that divides 19626 without a remainder.

1, 3, 5, 7, 11, 15, 17, 21, 33, 35, 51, 55, 77, 85, 105, 119, 165, 187, 231, 255, 357, 385, 561, 595, 935, 1155, 1309, 1785, 2805, 3927, 6545

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19626 and 19635. The biggest common factor number is the GCF number.
So the greatest common factor 19626 and 19635 is 3.

Also check out the Least Common Multiple of 19626 and 19635