What is the Greatest Common Factor of 1491 and 1500?

Greatest common factor (GCF) of 1491 and 1500 is 3.

GCF(1491,1500) = 3

We will now calculate the prime factors of 1491 and 1500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1491 and 1500.

How to find the GCF of 1491 and 1500?

We will first find the prime factorization of 1491 and 1500. After we will calculate the factors of 1491 and 1500 and find the biggest common factor number .

Step-1: Prime Factorization of 1491

Prime factors of 1491 are 3, 7, 71. Prime factorization of 1491 in exponential form is:

1491 = 3¹ × 7¹ × 71¹

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 1491

List of positive integer factors of 1491 that divides 1491 without a remainder.

1, 3, 7, 21, 71, 213, 497

Step-4: Factors of 1500

List of positive integer factors of 1500 that divides 1491 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 1491 and 1500. The biggest common factor number is the GCF number.
So the greatest common factor 1491 and 1500 is 3.

Also check out the Least Common Multiple of 1491 and 1500