Greatest Common Factor of 303 and 309

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 303, 309 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 303 and 309 is 3.

GCF(303,309) = 3

GCF of 303 and 309

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

GCF of:
and

Greatest Common Factor of 303 and 309

GCF of 303 and 309 is 3

Prime Factorization of 303


3 303
101 101
1

Prime factors of 303 are 3,101. Prime factorization of 303 in exponential form is:

303 = 31×1011

Prime Factorization of 309


3 309
103 103
1

Prime factors of 309 are 3,103. Prime factorization of 309 in exponential form is:

309 = 31×1031

∴ So by taking common prime factors GCF of 303 and 309 is 3

Greatest Common Factor of 303 and 309 by matching factors method

Factors of 303

List of positive integer factors of 303 that divides 303 without a remainder.

1,3,101,303

Factors of 309

List of positive integer factors of 309 that divides 309 without a remainder.

1,3,103,309

Greatest Common Factor

We found the factors and prime factorization of 303 and 309. The biggest common factor number is the GCF number.
So the greatest common factor 303 and 309 is 3.

Also check out the Least Common Multiple of 303 and 309

Properties of GCF 303 and 309

(i) The GCF of 303 and 309 is associative

GCF of 303 and 309 = GCF of 309 and 303

Related Greatest Common Factor of 303

Related Greatest Common Factor of 309

Frequently Asked Questions on GCF of 303 and 309

1. What is the GCF of 303 and 309?

Answer: GCF of 303 and 309 is 3.

2. What are the Factors of 303?

Answer: Factors of 303 are 1, 3, 101, 303. There are 4 integers that are factors of 303. The greatest factor of 303 is 303.

3. What are the Factors of 309?

Answer: Factors of 309 are 1, 3, 103, 309. There are 4 integers that are factors of 309. The greatest factor of 309 is 309.

4. How to Find the GCF of 303 and 309?

Answer:

Greatest Common Factor of 303 and 309 = 3

Step 1: Find the prime factorization of 303

303 = 3 x 101

Step 2: Find the prime factorization of 309

309 = 3 x 103

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3

Step 4: Therefore, the greatest common factor of 303 and 309 is 3