What is the Greatest Common Factor of 1538 and 1552?

Greatest common factor (GCF) of 1538 and 1552 is 2.

GCF(1538,1552) = 2

We will now calculate the prime factors of 1538 and 1552, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1538 and 1552.

How to find the GCF of 1538 and 1552?

We will first find the prime factorization of 1538 and 1552. After we will calculate the factors of 1538 and 1552 and find the biggest common factor number .

Step-1: Prime Factorization of 1538

Prime factors of 1538 are 2, 769. Prime factorization of 1538 in exponential form is:

1538 = 2¹ × 769¹

Step-2: Prime Factorization of 1552

Prime factors of 1552 are 2, 97. Prime factorization of 1552 in exponential form is:

1552 = 2⁴ × 97¹

Step-3: Factors of 1538

List of positive integer factors of 1538 that divides 1538 without a remainder.

1, 2, 769

Step-4: Factors of 1552

List of positive integer factors of 1552 that divides 1538 without a remainder.

1, 2, 4, 8, 16, 97, 194, 388, 776

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1538 and 1552. The biggest common factor number is the GCF number.
So the greatest common factor 1538 and 1552 is 2.

Also check out the Least Common Multiple of 1538 and 1552