What is the Greatest Common Factor of 1520 and 1538?

Greatest common factor (GCF) of 1520 and 1538 is 2.

GCF(1520,1538) = 2

We will now calculate the prime factors of 1520 and 1538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1520 and 1538.

How to find the GCF of 1520 and 1538?

We will first find the prime factorization of 1520 and 1538. After we will calculate the factors of 1520 and 1538 and find the biggest common factor number .

Step-1: Prime Factorization of 1520

Prime factors of 1520 are 2, 5, 19. Prime factorization of 1520 in exponential form is:

1520 = 2⁴ × 5¹ × 19¹

Step-2: Prime Factorization of 1538

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

1538 = 2¹ × 769¹

Step-3: Factors of 1520

List of positive integer factors of 1520 that divides 1520 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 80, 95, 152, 190, 304, 380, 760

Step-4: Factors of 1538

List of positive integer factors of 1538 that divides 1520 without a remainder.

1, 2, 769

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1520 and 1538. The biggest common factor number is the GCF number.
So the greatest common factor 1520 and 1538 is 2.

Also check out the Least Common Multiple of 1520 and 1538