What is the Greatest Common Factor of 17628 and 17638?

Greatest common factor (GCF) of 17628 and 17638 is 2.

GCF(17628,17638) = 2

We will now calculate the prime factors of 17628 and 17638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17628 and 17638.

How to find the GCF of 17628 and 17638?

We will first find the prime factorization of 17628 and 17638. After we will calculate the factors of 17628 and 17638 and find the biggest common factor number .

Step-1: Prime Factorization of 17628

Prime factors of 17628 are 2, 3, 13, 113. Prime factorization of 17628 in exponential form is:

17628 = 2² × 3¹ × 13¹ × 113¹

Step-2: Prime Factorization of 17638

Prime factors of 17638 are 2, 8819. Prime factorization of 17638 in exponential form is:

17638 = 2¹ × 8819¹

Step-3: Factors of 17628

List of positive integer factors of 17628 that divides 17628 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 113, 156, 226, 339, 452, 678, 1356, 1469, 2938, 4407, 5876, 8814

Step-4: Factors of 17638

List of positive integer factors of 17638 that divides 17628 without a remainder.

1, 2, 8819

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17628 and 17638. The biggest common factor number is the GCF number.
So the greatest common factor 17628 and 17638 is 2.

Also check out the Least Common Multiple of 17628 and 17638