Greatest Common Factor of 30 and 32

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, 32 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 30 and 32 is 2.

GCF(30,32) = 2

GCF of 30 and 32

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

GCF of:
and

Greatest Common Factor of 30 and 32

GCF of 30 and 32 is 2

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 32


2 32
2 16
2 8
2 4
2 2
1

Prime factors of 32 are 2. Prime factorization of 32 in exponential form is:

32 = 25

∴ So by taking common prime factors GCF of 30 and 32 is 2

Greatest Common Factor of 30 and 32 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 32

List of positive integer factors of 32 that divides 32 without a remainder.

1,2,4,8,16,32

Greatest Common Factor

We found the factors and prime factorization of 30 and 32. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 32 is 2.

Also check out the Least Common Multiple of 30 and 32

Properties of GCF 30 and 32

(i) The GCF of 30 and 32 is associative

GCF of 30 and 32 = GCF of 32 and 30

Related Greatest Common Factor of 30

Related Greatest Common Factor of 32

Frequently Asked Questions on GCF of 30 and 32

1. What is the GCF of 30 and 32?

Answer: GCF of 30 and 32 is 2.

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 32?

Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.

4. How to Find the GCF of 30 and 32?

Answer:

Greatest Common Factor of 30 and 32 = 2

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

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 30 and 32 is 2