Greatest Common Factor of 272 and 280

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 272, 280 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 272 and 280 is 8.

GCF(272,280) = 8

GCF of 272 and 280

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

GCF of:
and

Greatest Common Factor of 272 and 280

GCF of 272 and 280 is 8

Prime Factorization of 272


2 272
2 136
2 68
2 34
17 17
1

Prime factors of 272 are 2,17. Prime factorization of 272 in exponential form is:

272 = 24×171

Prime Factorization of 280


2 280
2 140
2 70
5 35
7 7
1

Prime factors of 280 are 2,5,7. Prime factorization of 280 in exponential form is:

280 = 23×51×71

∴ So by taking common prime factors GCF of 272 and 280 is 8

Greatest Common Factor of 272 and 280 by matching factors method

Factors of 272

List of positive integer factors of 272 that divides 272 without a remainder.

1,2,4,8,16,17,34,68,136,272

Factors of 280

List of positive integer factors of 280 that divides 280 without a remainder.

1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280

Greatest Common Factor

We found the factors and prime factorization of 272 and 280. The biggest common factor number is the GCF number.
So the greatest common factor 272 and 280 is 8.

Also check out the Least Common Multiple of 272 and 280

Properties of GCF 272 and 280

(i) The GCF of 272 and 280 is associative

GCF of 272 and 280 = GCF of 280 and 272

Related Greatest Common Factor of 272

Related Greatest Common Factor of 280

Frequently Asked Questions on GCF of 272 and 280

1. What is the GCF of 272 and 280?

Answer: GCF of 272 and 280 is 8.

2. What are the Factors of 272?

Answer: Factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272. There are 10 integers that are factors of 272. The greatest factor of 272 is 272.

3. What are the Factors of 280?

Answer: Factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280. There are 16 integers that are factors of 280. The greatest factor of 280 is 280.

4. How to Find the GCF of 272 and 280?

Answer:

Greatest Common Factor of 272 and 280 = 8

Step 1: Find the prime factorization of 272

272 = 2 x 2 x 2 x 2 x 17

Step 2: Find the prime factorization of 280

280 = 2 x 2 x 2 x 5 x 7

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 272 and 280 is 8