Greatest Common Factor of 208 and 212

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, 212 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 208 and 212 is 4.

GCF(208,212) = 4

GCF of 208 and 212

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

GCF of:
and

Greatest Common Factor of 208 and 212

GCF of 208 and 212 is 4

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 212


2 212
2 106
53 53
1

Prime factors of 212 are 2,53. Prime factorization of 212 in exponential form is:

212 = 22×531

∴ So by taking common prime factors GCF of 208 and 212 is 4

Greatest Common Factor of 208 and 212 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 212

List of positive integer factors of 212 that divides 212 without a remainder.

1,2,4,53,106,212

Greatest Common Factor

We found the factors and prime factorization of 208 and 212. The biggest common factor number is the GCF number.
So the greatest common factor 208 and 212 is 4.

Also check out the Least Common Multiple of 208 and 212

Properties of GCF 208 and 212

(i) The GCF of 208 and 212 is associative

GCF of 208 and 212 = GCF of 212 and 208

Related Greatest Common Factor of 208

Related Greatest Common Factor of 212

Frequently Asked Questions on GCF of 208 and 212

1. What is the GCF of 208 and 212?

Answer: GCF of 208 and 212 is 4.

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 212?

Answer: Factors of 212 are 1, 2, 4, 53, 106, 212. There are 6 integers that are factors of 212. The greatest factor of 212 is 212.

4. How to Find the GCF of 208 and 212?

Answer:

Greatest Common Factor of 208 and 212 = 4

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 212

212 = 2 x 2 x 53

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 208 and 212 is 4