Greatest Common Factor of 196 and 203

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 196, 203 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 196 and 203 is 7.

GCF(196,203) = 7

GCF of 196 and 203

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

GCF of:
and

Greatest Common Factor of 196 and 203

GCF of 196 and 203 is 7

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

Prime Factorization of 203


7 203
29 29
1

Prime factors of 203 are 7,29. Prime factorization of 203 in exponential form is:

203 = 71×291

∴ So by taking common prime factors GCF of 196 and 203 is 7

Greatest Common Factor of 196 and 203 by matching factors method

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

Factors of 203

List of positive integer factors of 203 that divides 203 without a remainder.

1,7,29,203

Greatest Common Factor

We found the factors and prime factorization of 196 and 203. The biggest common factor number is the GCF number.
So the greatest common factor 196 and 203 is 7.

Also check out the Least Common Multiple of 196 and 203

Properties of GCF 196 and 203

(i) The GCF of 196 and 203 is associative

GCF of 196 and 203 = GCF of 203 and 196

Related Greatest Common Factor of 196

Related Greatest Common Factor of 203

Frequently Asked Questions on GCF of 196 and 203

1. What is the GCF of 196 and 203?

Answer: GCF of 196 and 203 is 7.

2. 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.

3. What are the Factors of 203?

Answer: Factors of 203 are 1, 7, 29, 203. There are 4 integers that are factors of 203. The greatest factor of 203 is 203.

4. How to Find the GCF of 196 and 203?

Answer:

Greatest Common Factor of 196 and 203 = 7

Step 1: Find the prime factorization of 196

196 = 2 x 2 x 7 x 7

Step 2: Find the prime factorization of 203

203 = 7 x 29

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 196 and 203 is 7