What is the Greatest Common Factor of 13538 and 13552?

Greatest common factor (GCF) of 13538 and 13552 is 14.

GCF(13538,13552) = 14

We will now calculate the prime factors of 13538 and 13552, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13538 and 13552.

How to find the GCF of 13538 and 13552?

We will first find the prime factorization of 13538 and 13552. After we will calculate the factors of 13538 and 13552 and find the biggest common factor number .

Step-1: Prime Factorization of 13538

Prime factors of 13538 are 2, 7, 967. Prime factorization of 13538 in exponential form is:

13538 = 2¹ × 7¹ × 967¹

Step-2: Prime Factorization of 13552

Prime factors of 13552 are 2, 7, 11. Prime factorization of 13552 in exponential form is:

13552 = 2⁴ × 7¹ × 11²

Step-3: Factors of 13538

List of positive integer factors of 13538 that divides 13538 without a remainder.

1, 2, 7, 14, 967, 1934, 6769

Step-4: Factors of 13552

List of positive integer factors of 13552 that divides 13538 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 44, 56, 77, 88, 112, 121, 154, 176, 242, 308, 484, 616, 847, 968, 1232, 1694, 1936, 3388, 6776

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13538 and 13552. The biggest common factor number is the GCF number.
So the greatest common factor 13538 and 13552 is 14.

Also check out the Least Common Multiple of 13538 and 13552