Greatest Common Factor of 168 and 175

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, 175 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 168 and 175 is 7.

GCF(168,175) = 7

GCF of 168 and 175

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

GCF of:
and

Greatest Common Factor of 168 and 175

GCF of 168 and 175 is 7

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 175


5 175
5 35
7 7
1

Prime factors of 175 are 5,7. Prime factorization of 175 in exponential form is:

175 = 52×71

∴ So by taking common prime factors GCF of 168 and 175 is 7

Greatest Common Factor of 168 and 175 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 175

List of positive integer factors of 175 that divides 175 without a remainder.

1,5,7,25,35,175

Greatest Common Factor

We found the factors and prime factorization of 168 and 175. The biggest common factor number is the GCF number.
So the greatest common factor 168 and 175 is 7.

Also check out the Least Common Multiple of 168 and 175

Properties of GCF 168 and 175

(i) The GCF of 168 and 175 is associative

GCF of 168 and 175 = GCF of 175 and 168

Related Greatest Common Factor of 168

Related Greatest Common Factor of 175

Frequently Asked Questions on GCF of 168 and 175

1. What is the GCF of 168 and 175?

Answer: GCF of 168 and 175 is 7.

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 175?

Answer: Factors of 175 are 1, 5, 7, 25, 35, 175. There are 6 integers that are factors of 175. The greatest factor of 175 is 175.

4. How to Find the GCF of 168 and 175?

Answer:

Greatest Common Factor of 168 and 175 = 7

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 175

175 = 5 x 5 x 7

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

GCF = 7

Step 4: Therefore, the greatest common factor of 168 and 175 is 7