What is the Greatest Common Factor of 1500 and 1504?

Greatest common factor (GCF) of 1500 and 1504 is 4.

GCF(1500,1504) = 4

We will now calculate the prime factors of 1500 and 1504, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1500 and 1504.

How to find the GCF of 1500 and 1504?

We will first find the prime factorization of 1500 and 1504. After we will calculate the factors of 1500 and 1504 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 1504

Prime factors of 1504 are 2, 47. Prime factorization of 1504 in exponential form is:

1504 = 2⁵ × 47¹

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 1504

List of positive integer factors of 1504 that divides 1500 without a remainder.

1, 2, 4, 8, 16, 32, 47, 94, 188, 376, 752

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1500 and 1504. The biggest common factor number is the GCF number.
So the greatest common factor 1500 and 1504 is 4.

Also check out the Least Common Multiple of 1500 and 1504