Greatest Common Factor of 1208 and 1214

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 1208, 1214 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1208 and 1214 is 2.

GCF(1208,1214) = 2

GCF of 1208 and 1214

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

GCF of:
and

Greatest Common Factor of 1208 and 1214

GCF of 1208 and 1214 is 2

Prime Factorization of 1208


2 1208
2 604
2 302
151 151
1

Prime factors of 1208 are 2,151. Prime factorization of 1208 in exponential form is:

1208 = 23×1511

Prime Factorization of 1214


2 1214
607 607
1

Prime factors of 1214 are 2,607. Prime factorization of 1214 in exponential form is:

1214 = 21×6071

∴ So by taking common prime factors GCF of 1208 and 1214 is 2

Greatest Common Factor of 1208 and 1214 by matching factors method

Factors of 1208

List of positive integer factors of 1208 that divides 1208 without a remainder.

1,2,4,8,151,302,604,1208

Factors of 1214

List of positive integer factors of 1214 that divides 1214 without a remainder.

1,2,607,1214

Greatest Common Factor

We found the factors and prime factorization of 1208 and 1214. The biggest common factor number is the GCF number.
So the greatest common factor 1208 and 1214 is 2.

Also check out the Least Common Multiple of 1208 and 1214

Properties of GCF 1208 and 1214

(i) The GCF of 1208 and 1214 is associative

GCF of 1208 and 1214 = GCF of 1214 and 1208

Related Greatest Common Factor of 1208

Related Greatest Common Factor of 1214

Frequently Asked Questions on GCF of 1208 and 1214

1. What is the GCF of 1208 and 1214?

Answer: GCF of 1208 and 1214 is 2.

2. What are the Factors of 1208?

Answer: Factors of 1208 are 1, 2, 4, 8, 151, 302, 604, 1208. There are 8 integers that are factors of 1208. The greatest factor of 1208 is 1208.

3. What are the Factors of 1214?

Answer: Factors of 1214 are 1, 2, 607, 1214. There are 4 integers that are factors of 1214. The greatest factor of 1214 is 1214.

4. How to Find the GCF of 1208 and 1214?

Answer:

Greatest Common Factor of 1208 and 1214 = 2

Step 1: Find the prime factorization of 1208

1208 = 2 x 2 x 2 x 151

Step 2: Find the prime factorization of 1214

1214 = 2 x 607

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 1208 and 1214 is 2