Greatest Common Factor of 448 and 456

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 448, 456 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 448 and 456 is 8.

GCF(448,456) = 8

GCF of 448 and 456

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 448 and 456

GCF of 448 and 456 is 8

Prime Factorization of 448


2 448
2 224
2 112
2 56
2 28
2 14
7 7
1

Prime factors of 448 are 2,7. Prime factorization of 448 in exponential form is:

448 = 26×71

Prime Factorization of 456


2 456
2 228
2 114
3 57
19 19
1

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

456 = 23×31×191

∴ So by taking common prime factors GCF of 448 and 456 is 8

Greatest Common Factor of 448 and 456 by matching factors method

Factors of 448

List of positive integer factors of 448 that divides 448 without a remainder.

1,2,4,7,8,14,16,28,32,56,64,112,224,448

Factors of 456

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

1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456

Greatest Common Factor

We found the factors and prime factorization of 448 and 456. The biggest common factor number is the GCF number.
So the greatest common factor 448 and 456 is 8.

Also check out the Least Common Multiple of 448 and 456

Properties of GCF 448 and 456

(i) The GCF of 448 and 456 is associative

GCF of 448 and 456 = GCF of 456 and 448

Related Greatest Common Factor of 448

Related Greatest Common Factor of 456

Frequently Asked Questions on GCF of 448 and 456

1. What is the GCF of 448 and 456?

Answer: GCF of 448 and 456 is 8.

2. What are the Factors of 448?

Answer: Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448. There are 14 integers that are factors of 448. The greatest factor of 448 is 448.

3. What are the Factors of 456?

Answer: Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456. There are 16 integers that are factors of 456. The greatest factor of 456 is 456.

4. How to Find the GCF of 448 and 456?

Answer:

Greatest Common Factor of 448 and 456 = 8

Step 1: Find the prime factorization of 448

448 = 2 x 2 x 2 x 2 x 2 x 2 x 7

Step 2: Find the prime factorization of 456

456 = 2 x 2 x 2 x 3 x 19

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 448 and 456 is 8