Greatest Common Factor of 189 and 196

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 189, 196 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 189 and 196 is 7.

GCF(189,196) = 7

GCF of 189 and 196

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

GCF of:
and

Greatest Common Factor of 189 and 196

GCF of 189 and 196 is 7

Prime Factorization of 189


3 189
3 63
3 21
7 7
1

Prime factors of 189 are 3,7. Prime factorization of 189 in exponential form is:

189 = 33×71

Prime Factorization of 196


2 196
2 98
7 49
7 7
1

Prime factors of 196 are 2,7. Prime factorization of 196 in exponential form is:

196 = 22×72

∴ So by taking common prime factors GCF of 189 and 196 is 7

Greatest Common Factor of 189 and 196 by matching factors method

Factors of 189

List of positive integer factors of 189 that divides 189 without a remainder.

1,3,7,9,21,27,63,189

Factors of 196

List of positive integer factors of 196 that divides 196 without a remainder.

1,2,4,7,14,28,49,98,196

Greatest Common Factor

We found the factors and prime factorization of 189 and 196. The biggest common factor number is the GCF number.
So the greatest common factor 189 and 196 is 7.

Also check out the Least Common Multiple of 189 and 196

Properties of GCF 189 and 196

(i) The GCF of 189 and 196 is associative

GCF of 189 and 196 = GCF of 196 and 189

Related Greatest Common Factor of 189

Related Greatest Common Factor of 196

Frequently Asked Questions on GCF of 189 and 196

1. What is the GCF of 189 and 196?

Answer: GCF of 189 and 196 is 7.

2. What are the Factors of 189?

Answer: Factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189. There are 8 integers that are factors of 189. The greatest factor of 189 is 189.

3. What are the Factors of 196?

Answer: Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196. There are 9 integers that are factors of 196. The greatest factor of 196 is 196.

4. How to Find the GCF of 189 and 196?

Answer:

Greatest Common Factor of 189 and 196 = 7

Step 1: Find the prime factorization of 189

189 = 3 x 3 x 3 x 7

Step 2: Find the prime factorization of 196

196 = 2 x 2 x 7 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 189 and 196 is 7