Greatest Common Factor of 30 and 50

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 30, 50 i.e. 10 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 30 and 50 is 10.

GCF(30,50) = 10

GCF of 30 and 50

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

GCF of:
and

Greatest Common Factor of 30 and 50

GCF of 30 and 50 is 10

Prime Factorization of 30


2 30
3 15
5 5
1

Prime factors of 30 are 2,3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

Prime Factorization of 50


2 50
5 25
5 5
1

Prime factors of 50 are 2,5. Prime factorization of 50 in exponential form is:

50 = 21×52

∴ So by taking common prime factors GCF of 30 and 50 is 10

Greatest Common Factor of 30 and 50 by matching factors method

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

Factors of 50

List of positive integer factors of 50 that divides 50 without a remainder.

1,2,5,10,25,50

Greatest Common Factor

We found the factors and prime factorization of 30 and 50. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 50 is 10.

Also check out the Least Common Multiple of 30 and 50

Properties of GCF 30 and 50

(i) The GCF of 30 and 50 is associative

GCF of 30 and 50 = GCF of 50 and 30

Related Greatest Common Factor of 30

Related Greatest Common Factor of 50

Frequently Asked Questions on GCF of 30 and 50

1. What is the GCF of 30 and 50?

Answer: GCF of 30 and 50 is 10.

2. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

3. What are the Factors of 50?

Answer: Factors of 50 are 1, 2, 5, 10, 25, 50. There are 6 integers that are factors of 50. The greatest factor of 50 is 50.

4. How to Find the GCF of 30 and 50?

Answer:

Greatest Common Factor of 30 and 50 = 10

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 50

50 = 2 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 5 = 10

Step 4: Therefore, the greatest common factor of 30 and 50 is 10