Greatest Common Factor of 224 and 232

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

Greatest common factor (GCF) of 224 and 232 is 8.

GCF(224,232) = 8

GCF of 224 and 232

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

GCF of:
and

Greatest Common Factor of 224 and 232

GCF of 224 and 232 is 8

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 232


2 232
2 116
2 58
29 29
1

Prime factors of 232 are 2,29. Prime factorization of 232 in exponential form is:

232 = 23×291

∴ So by taking common prime factors GCF of 224 and 232 is 8

Greatest Common Factor of 224 and 232 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 232

List of positive integer factors of 232 that divides 232 without a remainder.

1,2,4,8,29,58,116,232

Greatest Common Factor

We found the factors and prime factorization of 224 and 232. The biggest common factor number is the GCF number.
So the greatest common factor 224 and 232 is 8.

Also check out the Least Common Multiple of 224 and 232

Properties of GCF 224 and 232

(i) The GCF of 224 and 232 is associative

GCF of 224 and 232 = GCF of 232 and 224

Related Greatest Common Factor of 224

Related Greatest Common Factor of 232

Frequently Asked Questions on GCF of 224 and 232

1. What is the GCF of 224 and 232?

Answer: GCF of 224 and 232 is 8.

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 232?

Answer: Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232. There are 8 integers that are factors of 232. The greatest factor of 232 is 232.

4. How to Find the GCF of 224 and 232?

Answer:

Greatest Common Factor of 224 and 232 = 8

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 232

232 = 2 x 2 x 2 x 29

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 224 and 232 is 8