Greatest Common Factor of 7208 and 7214

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 7208, 7214 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 7208 and 7214 is 2.

GCF(7208,7214) = 2

GCF of 7208 and 7214

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

GCF of:
and

Greatest Common Factor of 7208 and 7214

GCF of 7208 and 7214 is 2

Prime Factorization of 7208


2 7208
2 3604
2 1802
17 901
53 53
1

Prime factors of 7208 are 2,17,53. Prime factorization of 7208 in exponential form is:

7208 = 23×171×531

Prime Factorization of 7214


2 7214
3607 3607
1

Prime factors of 7214 are 2,3607. Prime factorization of 7214 in exponential form is:

7214 = 21×36071

∴ So by taking common prime factors GCF of 7208 and 7214 is 2

Greatest Common Factor of 7208 and 7214 by matching factors method

Factors of 7208

List of positive integer factors of 7208 that divides 7208 without a remainder.

1,2,4,8,17,34,53,68,106,136,212,424,901,1802,3604,7208

Factors of 7214

List of positive integer factors of 7214 that divides 7214 without a remainder.

1,2,3607,7214

Greatest Common Factor

We found the factors and prime factorization of 7208 and 7214. The biggest common factor number is the GCF number.
So the greatest common factor 7208 and 7214 is 2.

Also check out the Least Common Multiple of 7208 and 7214

Properties of GCF 7208 and 7214

(i) The GCF of 7208 and 7214 is associative

GCF of 7208 and 7214 = GCF of 7214 and 7208

Related Greatest Common Factor of 7208

Related Greatest Common Factor of 7214

Frequently Asked Questions on GCF of 7208 and 7214

1. What is the GCF of 7208 and 7214?

Answer: GCF of 7208 and 7214 is 2.

2. What are the Factors of 7208?

Answer: Factors of 7208 are 1, 2, 4, 8, 17, 34, 53, 68, 106, 136, 212, 424, 901, 1802, 3604, 7208. There are 16 integers that are factors of 7208. The greatest factor of 7208 is 7208.

3. What are the Factors of 7214?

Answer: Factors of 7214 are 1, 2, 3607, 7214. There are 4 integers that are factors of 7214. The greatest factor of 7214 is 7214.

4. How to Find the GCF of 7208 and 7214?

Answer:

Greatest Common Factor of 7208 and 7214 = 2

Step 1: Find the prime factorization of 7208

7208 = 2 x 2 x 2 x 17 x 53

Step 2: Find the prime factorization of 7214

7214 = 2 x 3607

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 7208 and 7214 is 2