Greatest Common Factor of 208 and 216

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 208, 216 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 208 and 216 is 8.

GCF(208,216) = 8

GCF of 208 and 216

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

GCF of:
and

Greatest Common Factor of 208 and 216

GCF of 208 and 216 is 8

Prime Factorization of 208


2 208
2 104
2 52
2 26
13 13
1

Prime factors of 208 are 2,13. Prime factorization of 208 in exponential form is:

208 = 24×131

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

∴ So by taking common prime factors GCF of 208 and 216 is 8

Greatest Common Factor of 208 and 216 by matching factors method

Factors of 208

List of positive integer factors of 208 that divides 208 without a remainder.

1,2,4,8,13,16,26,52,104,208

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

Greatest Common Factor

We found the factors and prime factorization of 208 and 216. The biggest common factor number is the GCF number.
So the greatest common factor 208 and 216 is 8.

Also check out the Least Common Multiple of 208 and 216

Properties of GCF 208 and 216

(i) The GCF of 208 and 216 is associative

GCF of 208 and 216 = GCF of 216 and 208

Related Greatest Common Factor of 208

Related Greatest Common Factor of 216

Frequently Asked Questions on GCF of 208 and 216

1. What is the GCF of 208 and 216?

Answer: GCF of 208 and 216 is 8.

2. What are the Factors of 208?

Answer: Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. There are 10 integers that are factors of 208. The greatest factor of 208 is 208.

3. 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.

4. How to Find the GCF of 208 and 216?

Answer:

Greatest Common Factor of 208 and 216 = 8

Step 1: Find the prime factorization of 208

208 = 2 x 2 x 2 x 2 x 13

Step 2: Find the prime factorization of 216

216 = 2 x 2 x 2 x 3 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 208 and 216 is 8