Greatest Common Factor of 216 and 224

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 216, 224 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 216 and 224 is 8.

GCF(216,224) = 8

GCF of 216 and 224

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

GCF of:
and

Greatest Common Factor of 216 and 224

GCF of 216 and 224 is 8

Prime Factorization of 216


2 216
2 108
2 54
3 27
3 9
3 3
1

Prime factors of 216 are 2,3. Prime factorization of 216 in exponential form is:

216 = 23×33

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

∴ So by taking common prime factors GCF of 216 and 224 is 8

Greatest Common Factor of 216 and 224 by matching factors method

Factors of 216

List of positive integer factors of 216 that divides 216 without a remainder.

1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216

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

Greatest Common Factor

We found the factors and prime factorization of 216 and 224. The biggest common factor number is the GCF number.
So the greatest common factor 216 and 224 is 8.

Also check out the Least Common Multiple of 216 and 224

Properties of GCF 216 and 224

(i) The GCF of 216 and 224 is associative

GCF of 216 and 224 = GCF of 224 and 216

Related Greatest Common Factor of 216

Related Greatest Common Factor of 224

Frequently Asked Questions on GCF of 216 and 224

1. What is the GCF of 216 and 224?

Answer: GCF of 216 and 224 is 8.

2. What are the Factors of 216?

Answer: Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216. There are 16 integers that are factors of 216. The greatest factor of 216 is 216.

3. 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.

4. How to Find the GCF of 216 and 224?

Answer:

Greatest Common Factor of 216 and 224 = 8

Step 1: Find the prime factorization of 216

216 = 2 x 2 x 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 224

224 = 2 x 2 x 2 x 2 x 2 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 216 and 224 is 8