Greatest Common Factor of 168 and 174

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, 174 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 168 and 174 is 6.

GCF(168,174) = 6

GCF of 168 and 174

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

GCF of:
and

Greatest Common Factor of 168 and 174

GCF of 168 and 174 is 6

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 174


2 174
3 87
29 29
1

Prime factors of 174 are 2,3,29. Prime factorization of 174 in exponential form is:

174 = 21×31×291

∴ So by taking common prime factors GCF of 168 and 174 is 6

Greatest Common Factor of 168 and 174 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 174

List of positive integer factors of 174 that divides 174 without a remainder.

1,2,3,6,29,58,87,174

Greatest Common Factor

We found the factors and prime factorization of 168 and 174. The biggest common factor number is the GCF number.
So the greatest common factor 168 and 174 is 6.

Also check out the Least Common Multiple of 168 and 174

Properties of GCF 168 and 174

(i) The GCF of 168 and 174 is associative

GCF of 168 and 174 = GCF of 174 and 168

Related Greatest Common Factor of 168

Related Greatest Common Factor of 174

Frequently Asked Questions on GCF of 168 and 174

1. What is the GCF of 168 and 174?

Answer: GCF of 168 and 174 is 6.

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 174?

Answer: Factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174. There are 8 integers that are factors of 174. The greatest factor of 174 is 174.

4. How to Find the GCF of 168 and 174?

Answer:

Greatest Common Factor of 168 and 174 = 6

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 174

174 = 2 x 3 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 3 = 6

Step 4: Therefore, the greatest common factor of 168 and 174 is 6