What is the Greatest Common Factor of 1500 and 1520?

Greatest common factor (GCF) of 1500 and 1520 is 20.

GCF(1500,1520) = 20

We will now calculate the prime factors of 1500 and 1520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1500 and 1520.

How to find the GCF of 1500 and 1520?

We will first find the prime factorization of 1500 and 1520. After we will calculate the factors of 1500 and 1520 and find the biggest common factor number .

Step-1: Prime Factorization of 1500

Prime factors of 1500 are 2, 3, 5. Prime factorization of 1500 in exponential form is:

1500 = 2² × 3¹ × 5³

Step-2: 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-3: Factors of 1500

List of positive integer factors of 1500 that divides 1500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750

Step-4: Factors of 1520

List of positive integer factors of 1520 that divides 1500 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1500 and 1520. The biggest common factor number is the GCF number.
So the greatest common factor 1500 and 1520 is 20.

Also check out the Least Common Multiple of 1500 and 1520