What is the Greatest Common Factor of 1497 and 1512?

Greatest common factor (GCF) of 1497 and 1512 is 3.

GCF(1497,1512) = 3

We will now calculate the prime factors of 1497 and 1512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1497 and 1512.

How to find the GCF of 1497 and 1512?

We will first find the prime factorization of 1497 and 1512. After we will calculate the factors of 1497 and 1512 and find the biggest common factor number .

Step-1: Prime Factorization of 1497

Prime factors of 1497 are 3, 499. Prime factorization of 1497 in exponential form is:

1497 = 3¹ × 499¹

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 1497

List of positive integer factors of 1497 that divides 1497 without a remainder.

1, 3, 499

Step-4: Factors of 1512

List of positive integer factors of 1512 that divides 1497 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 1497 and 1512. The biggest common factor number is the GCF number.
So the greatest common factor 1497 and 1512 is 3.

Also check out the Least Common Multiple of 1497 and 1512