What is the Greatest Common Factor of 1538 and 1548?

Greatest common factor (GCF) of 1538 and 1548 is 2.

GCF(1538,1548) = 2

We will now calculate the prime factors of 1538 and 1548, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1538 and 1548.

How to find the GCF of 1538 and 1548?

We will first find the prime factorization of 1538 and 1548. After we will calculate the factors of 1538 and 1548 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 1548

Prime factors of 1548 are 2, 3, 43. Prime factorization of 1548 in exponential form is:

1548 = 2² × 3² × 43¹

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 1548

List of positive integer factors of 1548 that divides 1538 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 43, 86, 129, 172, 258, 387, 516, 774

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1538 and 1548. The biggest common factor number is the GCF number.
So the greatest common factor 1538 and 1548 is 2.

Also check out the Least Common Multiple of 1538 and 1548