Greatest Common Factor of 32 and 34

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 32, 34 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 32 and 34 is 2.

GCF(32,34) = 2

GCF of 32 and 34

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

GCF of:
and

Greatest Common Factor of 32 and 34

GCF of 32 and 34 is 2

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

Prime Factorization of 34


2 34
17 17
1

Prime factors of 34 are 2.Prime factorization of 34 in exponential form is:

34 = 21×171

∴ So by taking common prime factors GCF of 32 and 34 is 2

Greatest Common Factor of 32 and 34 by matching factors method

Factors of 32

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

1,2,4,8,16,32

Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1,2,17,34

Greatest Common Factor

We found the factors and prime factorization of 32 and 34. The biggest common factor number is the GCF number.
So the greatest common factor 32 and 34 is 2.

Also check out the Least Common Multiple of 32 and 34

Properties of GCF 32 and 34

(i) The GCF of 32 and 34 is associative

GCF of 32 and 34 = GCF of 34 and 32

Related Greatest Common Factor of 32

Related Greatest Common Factor of 34

Frequently Asked Questions on GCF of 32 and 34

1. What is the GCF of 32 and 34?

Answer: GCF of 32 and 34 is 2.

2. 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.

3. What are the Factors of 34?

Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.

4. How to Find the GCF of 32 and 34?

Answer:

Greatest Common Factor of 32 and 34 = 2

Step 1: Find the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 34

34 = 2 x 17

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 32 and 34 is 2