What is the Greatest Common Factor of 19635 and 19652?

Greatest common factor (GCF) of 19635 and 19652 is 17.

GCF(19635,19652) = 17

We will now calculate the prime factors of 19635 and 19652, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19635 and 19652.

How to find the GCF of 19635 and 19652?

We will first find the prime factorization of 19635 and 19652. After we will calculate the factors of 19635 and 19652 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19652

Prime factors of 19652 are 2, 17. Prime factorization of 19652 in exponential form is:

19652 = 2² × 17³

Step-3: Factors of 19635

List of positive integer factors of 19635 that divides 19635 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

Step-4: Factors of 19652

List of positive integer factors of 19652 that divides 19635 without a remainder.

1, 2, 4, 17, 34, 68, 289, 578, 1156, 4913, 9826

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19635 and 19652. The biggest common factor number is the GCF number.
So the greatest common factor 19635 and 19652 is 17.

Also check out the Least Common Multiple of 19635 and 19652