Greatest Common Factor of 172 and 176

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

Greatest common factor (GCF) of 172 and 176 is 4.

GCF(172,176) = 4

GCF of 172 and 176

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

GCF of:
and

Greatest Common Factor of 172 and 176

GCF of 172 and 176 is 4

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 176


2 176
2 88
2 44
2 22
11 11
1

Prime factors of 176 are 2,11. Prime factorization of 176 in exponential form is:

176 = 24×111

∴ So by taking common prime factors GCF of 172 and 176 is 4

Greatest Common Factor of 172 and 176 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 176

List of positive integer factors of 176 that divides 176 without a remainder.

1,2,4,8,11,16,22,44,88,176

Greatest Common Factor

We found the factors and prime factorization of 172 and 176. The biggest common factor number is the GCF number.
So the greatest common factor 172 and 176 is 4.

Also check out the Least Common Multiple of 172 and 176

Properties of GCF 172 and 176

(i) The GCF of 172 and 176 is associative

GCF of 172 and 176 = GCF of 176 and 172

Related Greatest Common Factor of 172

Related Greatest Common Factor of 176

Frequently Asked Questions on GCF of 172 and 176

1. What is the GCF of 172 and 176?

Answer: GCF of 172 and 176 is 4.

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 176?

Answer: Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176. There are 10 integers that are factors of 176. The greatest factor of 176 is 176.

4. How to Find the GCF of 172 and 176?

Answer:

Greatest Common Factor of 172 and 176 = 4

Step 1: Find the prime factorization of 172

172 = 2 x 2 x 43

Step 2: Find the prime factorization of 176

176 = 2 x 2 x 2 x 2 x 11

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 172 and 176 is 4