Greatest Common Factor of 174 and 182

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 174, 182 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 174 and 182 is 2.

GCF(174,182) = 2

GCF of 174 and 182

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

GCF of:
and

Greatest Common Factor of 174 and 182

GCF of 174 and 182 is 2

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

Prime Factorization of 182


2 182
7 91
13 13
1

Prime factors of 182 are 2,7,13. Prime factorization of 182 in exponential form is:

182 = 21×71×131

∴ So by taking common prime factors GCF of 174 and 182 is 2

Greatest Common Factor of 174 and 182 by matching factors method

Factors of 174

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

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

Factors of 182

List of positive integer factors of 182 that divides 182 without a remainder.

1,2,7,13,14,26,91,182

Greatest Common Factor

We found the factors and prime factorization of 174 and 182. The biggest common factor number is the GCF number.
So the greatest common factor 174 and 182 is 2.

Also check out the Least Common Multiple of 174 and 182

Properties of GCF 174 and 182

(i) The GCF of 174 and 182 is associative

GCF of 174 and 182 = GCF of 182 and 174

Related Greatest Common Factor of 174

Related Greatest Common Factor of 182

Frequently Asked Questions on GCF of 174 and 182

1. What is the GCF of 174 and 182?

Answer: GCF of 174 and 182 is 2.

2. 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.

3. What are the Factors of 182?

Answer: Factors of 182 are 1, 2, 7, 13, 14, 26, 91, 182. There are 8 integers that are factors of 182. The greatest factor of 182 is 182.

4. How to Find the GCF of 174 and 182?

Answer:

Greatest Common Factor of 174 and 182 = 2

Step 1: Find the prime factorization of 174

174 = 2 x 3 x 29

Step 2: Find the prime factorization of 182

182 = 2 x 7 x 13

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 174 and 182 is 2