What is the Greatest Common Factor of 1488 and 1500?

Greatest common factor (GCF) of 1488 and 1500 is 12.

GCF(1488,1500) = 12

We will now calculate the prime factors of 1488 and 1500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1488 and 1500.

How to find the GCF of 1488 and 1500?

We will first find the prime factorization of 1488 and 1500. After we will calculate the factors of 1488 and 1500 and find the biggest common factor number .

Step-1: Prime Factorization of 1488

Prime factors of 1488 are 2, 3, 31. Prime factorization of 1488 in exponential form is:

1488 = 2⁴ × 3¹ × 31¹

Step-2: 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-3: Factors of 1488

List of positive integer factors of 1488 that divides 1488 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 31, 48, 62, 93, 124, 186, 248, 372, 496, 744

Step-4: Factors of 1500

List of positive integer factors of 1500 that divides 1488 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1488 and 1500. The biggest common factor number is the GCF number.
So the greatest common factor 1488 and 1500 is 12.

Also check out the Least Common Multiple of 1488 and 1500