What is the Greatest Common Factor of 19628 and 19635?

Greatest common factor (GCF) of 19628 and 19635 is 7.

GCF(19628,19635) = 7

We will now calculate the prime factors of 19628 and 19635, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19628 and 19635.

How to find the GCF of 19628 and 19635?

We will first find the prime factorization of 19628 and 19635. After we will calculate the factors of 19628 and 19635 and find the biggest common factor number .

Step-1: Prime Factorization of 19628

Prime factors of 19628 are 2, 7, 701. Prime factorization of 19628 in exponential form is:

19628 = 2² × 7¹ × 701¹

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 19628

List of positive integer factors of 19628 that divides 19628 without a remainder.

1, 2, 4, 7, 14, 28, 701, 1402, 2804, 4907, 9814

Step-4: Factors of 19635

List of positive integer factors of 19635 that divides 19628 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 19628 and 19635. The biggest common factor number is the GCF number.
So the greatest common factor 19628 and 19635 is 7.

Also check out the Least Common Multiple of 19628 and 19635