Greatest Common Factor of 30 and 40

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

Greatest common factor (GCF) of 30 and 40 is 10.

GCF(30,40) = 10

GCF of 30 and 40

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

GCF of:
and

Greatest Common Factor of 30 and 40

GCF of 30 and 40 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 40


2 40
2 20
2 10
5 5
1

Prime factors of 40 are 2,5. Prime factorization of 40 in exponential form is:

40 = 23×51

∴ So by taking common prime factors GCF of 30 and 40 is 10

Greatest Common Factor of 30 and 40 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 40

List of positive integer factors of 40 that divides 40 without a remainder.

1,2,4,5,8,10,20,40

Greatest Common Factor

We found the factors and prime factorization of 30 and 40. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 40 is 10.

Also check out the Least Common Multiple of 30 and 40

Properties of GCF 30 and 40

(i) The GCF of 30 and 40 is associative

GCF of 30 and 40 = GCF of 40 and 30

Related Greatest Common Factor of 30

Related Greatest Common Factor of 40

Frequently Asked Questions on GCF of 30 and 40

1. What is the GCF of 30 and 40?

Answer: GCF of 30 and 40 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 40?

Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.

4. How to Find the GCF of 30 and 40?

Answer:

Greatest Common Factor of 30 and 40 = 10

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 40

40 = 2 x 2 x 2 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 40 is 10