# Greatest Common Factor of 200 and 202

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 200, 202 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 200 and 202 is 2.

GCF(200,202) = 2

## GCF of 200 and 202

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

GCF of:
and

### Greatest Common Factor of 200 and 202 by Prime factorization method

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

Prime Factorization of 202

 2 202 101 101 1

Prime factors of 202 are 2,101. Prime factorization of 202 in exponential form is:

202 = 21×1011

∴ So by taking common prime factors GCF of 200 and 202 is 2

### Greatest Common Factor of 200 and 202 by matching factors method

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

Factors of 202

List of positive integer factors of 202 that divides 202 without a remainder.

1,2,101,202

Greatest Common Factor

We found the factors and prime factorization of 200 and 202. The biggest common factor number is the GCF number.
So the greatest common factor 200 and 202 is 2.

Also check out the Least Common Multiple of 200 and 202

### Properties of GCF 200 and 202

(i) The GCF of 200 and 202 is associative

GCF of 200 and 202 = GCF of 202 and 200

### Frequently Asked Questions on GCF of 200 and 202

1. What is the GCF of 200 and 202?

Answer: GCF of 200 and 202 is 2.

2. 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.

3. What are the Factors of 202?

Answer: Factors of 202 are 1, 2, 101, 202. There are 4 integers that are factors of 202. The greatest factor of 202 is 202.

4. How to Find the GCF of 200 and 202?

Greatest Common Factor of 200 and 202 = 2

Step 1: Find the prime factorization of 200

200 = 2 x 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 202

202 = 2 x 101

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 200 and 202 is 2