Greatest Common Factor of 168 and 172

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 168, 172 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 168 and 172 is 4.

GCF(168,172) = 4

GCF of 168 and 172

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

GCF of:
and

Greatest Common Factor of 168 and 172

GCF of 168 and 172 is 4

Prime Factorization of 168


2 168
2 84
2 42
3 21
7 7
1

Prime factors of 168 are 2,3,7. Prime factorization of 168 in exponential form is:

168 = 23×31×71

Prime Factorization of 172


2 172
2 86
43 43
1

Prime factors of 172 are 2,43. Prime factorization of 172 in exponential form is:

172 = 22×431

∴ So by taking common prime factors GCF of 168 and 172 is 4

Greatest Common Factor of 168 and 172 by matching factors method

Factors of 168

List of positive integer factors of 168 that divides 168 without a remainder.

1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168

Factors of 172

List of positive integer factors of 172 that divides 172 without a remainder.

1,2,4,43,86,172

Greatest Common Factor

We found the factors and prime factorization of 168 and 172. The biggest common factor number is the GCF number.
So the greatest common factor 168 and 172 is 4.

Also check out the Least Common Multiple of 168 and 172

Properties of GCF 168 and 172

(i) The GCF of 168 and 172 is associative

GCF of 168 and 172 = GCF of 172 and 168

Related Greatest Common Factor of 168

Related Greatest Common Factor of 172

Frequently Asked Questions on GCF of 168 and 172

1. What is the GCF of 168 and 172?

Answer: GCF of 168 and 172 is 4.

2. What are the Factors of 168?

Answer: Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168. There are 16 integers that are factors of 168. The greatest factor of 168 is 168.

3. What are the Factors of 172?

Answer: Factors of 172 are 1, 2, 4, 43, 86, 172. There are 6 integers that are factors of 172. The greatest factor of 172 is 172.

4. How to Find the GCF of 168 and 172?

Answer:

Greatest Common Factor of 168 and 172 = 4

Step 1: Find the prime factorization of 168

168 = 2 x 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 172

172 = 2 x 2 x 43

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 168 and 172 is 4