Greatest Common Factor of 224 and 231

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 224, 231 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 224 and 231 is 7.

GCF(224,231) = 7

GCF of 224 and 231

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

GCF of:
and

Greatest Common Factor of 224 and 231

GCF of 224 and 231 is 7

Prime Factorization of 224


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

Prime factors of 224 are 2,7. Prime factorization of 224 in exponential form is:

224 = 25×71

Prime Factorization of 231


3 231
7 77
11 11
1

Prime factors of 231 are 3,7,11. Prime factorization of 231 in exponential form is:

231 = 31×71×111

∴ So by taking common prime factors GCF of 224 and 231 is 7

Greatest Common Factor of 224 and 231 by matching factors method

Factors of 224

List of positive integer factors of 224 that divides 224 without a remainder.

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

Factors of 231

List of positive integer factors of 231 that divides 231 without a remainder.

1,3,7,11,21,33,77,231

Greatest Common Factor

We found the factors and prime factorization of 224 and 231. The biggest common factor number is the GCF number.
So the greatest common factor 224 and 231 is 7.

Also check out the Least Common Multiple of 224 and 231

Properties of GCF 224 and 231

(i) The GCF of 224 and 231 is associative

GCF of 224 and 231 = GCF of 231 and 224

Related Greatest Common Factor of 224

Related Greatest Common Factor of 231

Frequently Asked Questions on GCF of 224 and 231

1. What is the GCF of 224 and 231?

Answer: GCF of 224 and 231 is 7.

2. What are the Factors of 224?

Answer: Factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224. There are 12 integers that are factors of 224. The greatest factor of 224 is 224.

3. What are the Factors of 231?

Answer: Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. There are 8 integers that are factors of 231. The greatest factor of 231 is 231.

4. How to Find the GCF of 224 and 231?

Answer:

Greatest Common Factor of 224 and 231 = 7

Step 1: Find the prime factorization of 224

224 = 2 x 2 x 2 x 2 x 2 x 7

Step 2: Find the prime factorization of 231

231 = 3 x 7 x 11

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

GCF = 7

Step 4: Therefore, the greatest common factor of 224 and 231 is 7