Greatest Common Factor of 280 and 288

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 280, 288 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 280 and 288 is 8.

GCF(280,288) = 8

GCF of 280 and 288

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

GCF of:
and

Greatest Common Factor of 280 and 288

GCF of 280 and 288 is 8

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

Prime Factorization of 288


2 288
2 144
2 72
2 36
2 18
3 9
3 3
1

Prime factors of 288 are 2,3. Prime factorization of 288 in exponential form is:

288 = 25×32

∴ So by taking common prime factors GCF of 280 and 288 is 8

Greatest Common Factor of 280 and 288 by matching factors method

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

Factors of 288

List of positive integer factors of 288 that divides 288 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288

Greatest Common Factor

We found the factors and prime factorization of 280 and 288. The biggest common factor number is the GCF number.
So the greatest common factor 280 and 288 is 8.

Also check out the Least Common Multiple of 280 and 288

Properties of GCF 280 and 288

(i) The GCF of 280 and 288 is associative

GCF of 280 and 288 = GCF of 288 and 280

Related Greatest Common Factor of 280

Related Greatest Common Factor of 288

Frequently Asked Questions on GCF of 280 and 288

1. What is the GCF of 280 and 288?

Answer: GCF of 280 and 288 is 8.

2. 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.

3. What are the Factors of 288?

Answer: Factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288. There are 18 integers that are factors of 288. The greatest factor of 288 is 288.

4. How to Find the GCF of 280 and 288?

Answer:

Greatest Common Factor of 280 and 288 = 8

Step 1: Find the prime factorization of 280

280 = 2 x 2 x 2 x 5 x 7

Step 2: Find the prime factorization of 288

288 = 2 x 2 x 2 x 2 x 2 x 3 x 3

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 280 and 288 is 8