What is the Greatest Common Factor of 437 and 456?

Greatest common factor (GCF) of 437 and 456 is 19.

GCF(437,456) = 19

We will now calculate the prime factors of 437 and 456, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 437 and 456.

How to find the GCF of 437 and 456?

We will first find the prime factorization of 437 and 456. After we will calculate the factors of 437 and 456 and find the biggest common factor number .

Step-1: Prime Factorization of 437

Prime factors of 437 are 19, 23. Prime factorization of 437 in exponential form is:

437 = 19¹ × 23¹

Step-2: 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-3: Factors of 437

List of positive integer factors of 437 that divides 437 without a remainder.

1, 19, 23

Step-4: Factors of 456

List of positive integer factors of 456 that divides 437 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 437 and 456. The biggest common factor number is the GCF number.
So the greatest common factor 437 and 456 is 19.

Also check out the Least Common Multiple of 437 and 456