Greatest Common Factor of 172 and 178

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 172, 178 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 172 and 178 is 2.

GCF(172,178) = 2

GCF of 172 and 178

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

GCF of:
and

Greatest Common Factor of 172 and 178

GCF of 172 and 178 is 2

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

Prime Factorization of 178


2 178
89 89
1

Prime factors of 178 are 2,89. Prime factorization of 178 in exponential form is:

178 = 21×891

∴ So by taking common prime factors GCF of 172 and 178 is 2

Greatest Common Factor of 172 and 178 by matching factors method

Factors of 172

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

1,2,4,43,86,172

Factors of 178

List of positive integer factors of 178 that divides 178 without a remainder.

1,2,89,178

Greatest Common Factor

We found the factors and prime factorization of 172 and 178. The biggest common factor number is the GCF number.
So the greatest common factor 172 and 178 is 2.

Also check out the Least Common Multiple of 172 and 178

Properties of GCF 172 and 178

(i) The GCF of 172 and 178 is associative

GCF of 172 and 178 = GCF of 178 and 172

Related Greatest Common Factor of 172

Related Greatest Common Factor of 178

Frequently Asked Questions on GCF of 172 and 178

1. What is the GCF of 172 and 178?

Answer: GCF of 172 and 178 is 2.

2. 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.

3. What are the Factors of 178?

Answer: Factors of 178 are 1, 2, 89, 178. There are 4 integers that are factors of 178. The greatest factor of 178 is 178.

4. How to Find the GCF of 172 and 178?

Answer:

Greatest Common Factor of 172 and 178 = 2

Step 1: Find the prime factorization of 172

172 = 2 x 2 x 43

Step 2: Find the prime factorization of 178

178 = 2 x 89

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

GCF = 2

Step 4: Therefore, the greatest common factor of 172 and 178 is 2