Greatest Common Factor of 214 and 220

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 214, 220 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 214 and 220 is 2.

GCF(214,220) = 2

GCF of 214 and 220

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

GCF of:
and

Greatest Common Factor of 214 and 220

GCF of 214 and 220 is 2

Prime Factorization of 214


2 214
107 107
1

Prime factors of 214 are 2,107. Prime factorization of 214 in exponential form is:

214 = 21×1071

Prime Factorization of 220


2 220
2 110
5 55
11 11
1

Prime factors of 220 are 2,5,11. Prime factorization of 220 in exponential form is:

220 = 22×51×111

∴ So by taking common prime factors GCF of 214 and 220 is 2

Greatest Common Factor of 214 and 220 by matching factors method

Factors of 214

List of positive integer factors of 214 that divides 214 without a remainder.

1,2,107,214

Factors of 220

List of positive integer factors of 220 that divides 220 without a remainder.

1,2,4,5,10,11,20,22,44,55,110,220

Greatest Common Factor

We found the factors and prime factorization of 214 and 220. The biggest common factor number is the GCF number.
So the greatest common factor 214 and 220 is 2.

Also check out the Least Common Multiple of 214 and 220

Properties of GCF 214 and 220

(i) The GCF of 214 and 220 is associative

GCF of 214 and 220 = GCF of 220 and 214

Related Greatest Common Factor of 214

Related Greatest Common Factor of 220

Frequently Asked Questions on GCF of 214 and 220

1. What is the GCF of 214 and 220?

Answer: GCF of 214 and 220 is 2.

2. What are the Factors of 214?

Answer: Factors of 214 are 1, 2, 107, 214. There are 4 integers that are factors of 214. The greatest factor of 214 is 214.

3. What are the Factors of 220?

Answer: Factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220. There are 12 integers that are factors of 220. The greatest factor of 220 is 220.

4. How to Find the GCF of 214 and 220?

Answer:

Greatest Common Factor of 214 and 220 = 2

Step 1: Find the prime factorization of 214

214 = 2 x 107

Step 2: Find the prime factorization of 220

220 = 2 x 2 x 5 x 11

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 214 and 220 is 2