What is the Greatest Common Factor of 456 and 464?

Greatest common factor (GCF) of 456 and 464 is 8.

GCF(456,464) = 8

We will now calculate the prime factors of 456 and 464, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 456 and 464.

How to find the GCF of 456 and 464?

We will first find the prime factorization of 456 and 464. After we will calculate the factors of 456 and 464 and find the biggest common factor number .

Step-1: Prime Factorization of 456

Prime factors of 456 are 2, 3, 19. Prime factorization of 456 in exponential form is:

456 = 2³ × 3¹ × 19¹

Step-2: Prime Factorization of 464

Prime factors of 464 are 2, 29. Prime factorization of 464 in exponential form is:

464 = 2⁴ × 29¹

Step-3: Factors of 456

List of positive integer factors of 456 that divides 456 without a remainder.

1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228

Step-4: Factors of 464

List of positive integer factors of 464 that divides 456 without a remainder.

1, 2, 4, 8, 16, 29, 58, 116, 232

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 456 and 464. The biggest common factor number is the GCF number.
So the greatest common factor 456 and 464 is 8.

Also check out the Least Common Multiple of 456 and 464