What is the Greatest Common Factor of 19617 and 19635?

Greatest common factor (GCF) of 19617 and 19635 is 3.

GCF(19617,19635) = 3

We will now calculate the prime factors of 19617 and 19635, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19617 and 19635.

How to find the GCF of 19617 and 19635?

We will first find the prime factorization of 19617 and 19635. After we will calculate the factors of 19617 and 19635 and find the biggest common factor number .

Step-1: Prime Factorization of 19617

Prime factors of 19617 are 3, 13, 503. Prime factorization of 19617 in exponential form is:

19617 = 3¹ × 13¹ × 503¹

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 19617

List of positive integer factors of 19617 that divides 19617 without a remainder.

1, 3, 13, 39, 503, 1509, 6539

Step-4: Factors of 19635

List of positive integer factors of 19635 that divides 19617 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 19617 and 19635. The biggest common factor number is the GCF number.
So the greatest common factor 19617 and 19635 is 3.

Also check out the Least Common Multiple of 19617 and 19635