What is the Greatest Common Factor of 1500 and 1512?

Greatest common factor (GCF) of 1500 and 1512 is 12.

GCF(1500,1512) = 12

We will now calculate the prime factors of 1500 and 1512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1500 and 1512.

How to find the GCF of 1500 and 1512?

We will first find the prime factorization of 1500 and 1512. After we will calculate the factors of 1500 and 1512 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 1512

Prime factors of 1512 are 2, 3, 7. Prime factorization of 1512 in exponential form is:

1512 = 2³ × 3³ × 7¹

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 1512

List of positive integer factors of 1512 that divides 1500 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1500 and 1512. The biggest common factor number is the GCF number.
So the greatest common factor 1500 and 1512 is 12.

Also check out the Least Common Multiple of 1500 and 1512