What is the Greatest Common Factor of 456 and 460?

Greatest common factor (GCF) of 456 and 460 is 4.

GCF(456,460) = 4

We will now calculate the prime factors of 456 and 460, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 456 and 460.

How to find the GCF of 456 and 460?

We will first find the prime factorization of 456 and 460. After we will calculate the factors of 456 and 460 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 460

Prime factors of 460 are 2, 5, 23. Prime factorization of 460 in exponential form is:

460 = 2² × 5¹ × 23¹

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 460

List of positive integer factors of 460 that divides 456 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 456 and 460. The biggest common factor number is the GCF number.
So the greatest common factor 456 and 460 is 4.

Also check out the Least Common Multiple of 456 and 460