Greatest Common Factor of 302 and 306

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 302, 306 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 302 and 306 is 2.

GCF(302,306) = 2

GCF of 302 and 306

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

GCF of:
and

Greatest Common Factor of 302 and 306

GCF of 302 and 306 is 2

Prime Factorization of 302


2 302
151 151
1

Prime factors of 302 are 2,151. Prime factorization of 302 in exponential form is:

302 = 21×1511

Prime Factorization of 306


2 306
3 153
3 51
17 17
1

Prime factors of 306 are 2,3,17. Prime factorization of 306 in exponential form is:

306 = 21×32×171

∴ So by taking common prime factors GCF of 302 and 306 is 2

Greatest Common Factor of 302 and 306 by matching factors method

Factors of 302

List of positive integer factors of 302 that divides 302 without a remainder.

1,2,151,302

Factors of 306

List of positive integer factors of 306 that divides 306 without a remainder.

1,2,3,6,9,17,18,34,51,102,153,306

Greatest Common Factor

We found the factors and prime factorization of 302 and 306. The biggest common factor number is the GCF number.
So the greatest common factor 302 and 306 is 2.

Also check out the Least Common Multiple of 302 and 306

Properties of GCF 302 and 306

(i) The GCF of 302 and 306 is associative

GCF of 302 and 306 = GCF of 306 and 302

Related Greatest Common Factor of 302

Related Greatest Common Factor of 306

Frequently Asked Questions on GCF of 302 and 306

1. What is the GCF of 302 and 306?

Answer: GCF of 302 and 306 is 2.

2. What are the Factors of 302?

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

3. What are the Factors of 306?

Answer: Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. There are 12 integers that are factors of 306. The greatest factor of 306 is 306.

4. How to Find the GCF of 302 and 306?

Answer:

Greatest Common Factor of 302 and 306 = 2

Step 1: Find the prime factorization of 302

302 = 2 x 151

Step 2: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

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 302 and 306 is 2