Greatest Common Factor of 294 and 300

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 294, 300 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 294 and 300 is 6.

GCF(294,300) = 6

GCF of 294 and 300

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

GCF of:
and

Greatest Common Factor of 294 and 300

GCF of 294 and 300 is 6

Prime Factorization of 294


2 294
3 147
7 49
7 7
1

Prime factors of 294 are 2,3,7. Prime factorization of 294 in exponential form is:

294 = 21×31×72

Prime Factorization of 300


2 300
2 150
3 75
5 25
5 5
1

Prime factors of 300 are 2,3,5. Prime factorization of 300 in exponential form is:

300 = 22×31×52

∴ So by taking common prime factors GCF of 294 and 300 is 6

Greatest Common Factor of 294 and 300 by matching factors method

Factors of 294

List of positive integer factors of 294 that divides 294 without a remainder.

1,2,3,6,7,14,21,42,49,98,147,294

Factors of 300

List of positive integer factors of 300 that divides 300 without a remainder.

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Greatest Common Factor

We found the factors and prime factorization of 294 and 300. The biggest common factor number is the GCF number.
So the greatest common factor 294 and 300 is 6.

Also check out the Least Common Multiple of 294 and 300

Properties of GCF 294 and 300

(i) The GCF of 294 and 300 is associative

GCF of 294 and 300 = GCF of 300 and 294

Related Greatest Common Factor of 294

Related Greatest Common Factor of 300

Frequently Asked Questions on GCF of 294 and 300

1. What is the GCF of 294 and 300?

Answer: GCF of 294 and 300 is 6.

2. What are the Factors of 294?

Answer: Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294. There are 12 integers that are factors of 294. The greatest factor of 294 is 294.

3. What are the Factors of 300?

Answer: Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300. There are 18 integers that are factors of 300. The greatest factor of 300 is 300.

4. How to Find the GCF of 294 and 300?

Answer:

Greatest Common Factor of 294 and 300 = 6

Step 1: Find the prime factorization of 294

294 = 2 x 3 x 7 x 7

Step 2: Find the prime factorization of 300

300 = 2 x 2 x 3 x 5 x 5

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 294 and 300 is 6