# Greatest Common Factor of 196 and 200

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 196, 200 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 196 and 200 is 4.

GCF(196,200) = 4

## GCF of 196 and 200

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

GCF of:
and

### Greatest Common Factor of 196 and 200 by Prime factorization method

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 200

 2 200 2 100 2 50 5 25 5 5 1

Prime factors of 200 are 2,5. Prime factorization of 200 in exponential form is:

200 = 23×52

∴ So by taking common prime factors GCF of 196 and 200 is 4

### Greatest Common Factor of 196 and 200 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 200

List of positive integer factors of 200 that divides 200 without a remainder.

1,2,4,5,8,10,20,25,40,50,100,200

Greatest Common Factor

We found the factors and prime factorization of 196 and 200. The biggest common factor number is the GCF number.
So the greatest common factor 196 and 200 is 4.

Also check out the Least Common Multiple of 196 and 200

### Properties of GCF 196 and 200

(i) The GCF of 196 and 200 is associative

GCF of 196 and 200 = GCF of 200 and 196

### Frequently Asked Questions on GCF of 196 and 200

1. What is the GCF of 196 and 200?

Answer: GCF of 196 and 200 is 4.

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 200?

Answer: Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. There are 12 integers that are factors of 200. The greatest factor of 200 is 200.

4. How to Find the GCF of 196 and 200?

Greatest Common Factor of 196 and 200 = 4

Step 1: Find the prime factorization of 196

196 = 2 x 2 x 7 x 7

Step 2: Find the prime factorization of 200

200 = 2 x 2 x 2 x 5 x 5

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 196 and 200 is 4 