What is the Greatest Common Factor of 1538 and 1558?

Greatest common factor (GCF) of 1538 and 1558 is 2.

GCF(1538,1558) = 2

We will now calculate the prime factors of 1538 and 1558, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1538 and 1558.

How to find the GCF of 1538 and 1558?

We will first find the prime factorization of 1538 and 1558. After we will calculate the factors of 1538 and 1558 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 1558

Prime factors of 1558 are 2, 19, 41. Prime factorization of 1558 in exponential form is:

1558 = 2¹ × 19¹ × 41¹

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 1558

List of positive integer factors of 1558 that divides 1538 without a remainder.

1, 2, 19, 38, 41, 82, 779

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1538 and 1558. The biggest common factor number is the GCF number.
So the greatest common factor 1538 and 1558 is 2.

Also check out the Least Common Multiple of 1538 and 1558