Euclid's Division Lemma Prime Factorisation Calculator Factors of a Number Calculator LCM Calculator GCF Calculator Factor Tree Calculator LCM of Decimals LCM of Fractions GCF of Decimals GCF of Fractions

Greatest Common Factor of 20 and 30

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 20, 30 i.e. 10 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 20 and 30 is 10.

GCF(20,30) = 10

GCF of 20 and 30

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

GCF of:
and

Greatest Common Factor of 20 and 30 by Prime factorization method

Prime Factorization of 20


2 20
2 10
5 5
1

Prime factors of 20 are 2,5. Prime factorization of 20 in exponential form is:

20 = 22×51

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

∴ So by taking common prime factors GCF of 20 and 30 is 10

Greatest Common Factor of 20 and 30 by matching factors method

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1,2,4,5,10,20

Factors of 30

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

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

Greatest Common Factor

We found the factors and prime factorization of 20 and 30. The biggest common factor number is the GCF number.
So the greatest common factor 20 and 30 is 10.

Also check out the Least Common Multiple of 20 and 30

Properties of GCF 20 and 30

(i) The GCF of 20 and 30 is associative

GCF of 20 and 30 = GCF of 30 and 20

Frequently Asked Questions on GCF of 20 and 30

1. What is the GCF of 20 and 30?

Answer: GCF of 20 and 30 is 10.

2. What are the Factors of 20?

Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.

3. 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.

4. How to Find the GCF of 20 and 30?

Answer:

Greatest Common Factor of 20 and 30 = 10

Step 1: Find the prime factorization of 20

20 = 2 x 2 x 5

Step 2: Find the prime factorization of 30

30 = 2 x 3 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 20 and 30 is 10