Greatest Common Factor of 298 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 298, 300 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 298 and 300 is 2.

GCF(298,300) = 2

GCF of 298 and 300

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

GCF of:
and

Greatest Common Factor of 298 and 300

GCF of 298 and 300 is 2

Prime Factorization of 298


2 298
149 149
1

Prime factors of 298 are 2,149. Prime factorization of 298 in exponential form is:

298 = 21×1491

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 298 and 300 is 2

Greatest Common Factor of 298 and 300 by matching factors method

Factors of 298

List of positive integer factors of 298 that divides 298 without a remainder.

1,2,149,298

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 298 and 300. The biggest common factor number is the GCF number.
So the greatest common factor 298 and 300 is 2.

Also check out the Least Common Multiple of 298 and 300

Properties of GCF 298 and 300

(i) The GCF of 298 and 300 is associative

GCF of 298 and 300 = GCF of 300 and 298

Related Greatest Common Factor of 298

Related Greatest Common Factor of 300

Frequently Asked Questions on GCF of 298 and 300

1. What is the GCF of 298 and 300?

Answer: GCF of 298 and 300 is 2.

2. What are the Factors of 298?

Answer: Factors of 298 are 1, 2, 149, 298. There are 4 integers that are factors of 298. The greatest factor of 298 is 298.

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 298 and 300?

Answer:

Greatest Common Factor of 298 and 300 = 2

Step 1: Find the prime factorization of 298

298 = 2 x 149

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

Step 4: Therefore, the greatest common factor of 298 and 300 is 2