Greatest Common Factor of 42 and 45

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 42, 45 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 42 and 45 is 3.

GCF(42,45) = 3

GCF of 42 and 45

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

GCF of:
and

Greatest Common Factor of 42 and 45

GCF of 42 and 45 is 3

Prime Factorization of 42


2 42
3 21
7 7
1

Prime factors of 42 are 2,3,7. Prime factorization of 42 in exponential form is:

42 = 21×31×71

Prime Factorization of 45


3 45
3 15
5 5
1

Prime factors of 45 are 3,5. Prime factorization of 45 in exponential form is:

45 = 32×51

∴ So by taking common prime factors GCF of 42 and 45 is 3

Greatest Common Factor of 42 and 45 by matching factors method

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1,2,3,6,7,14,21,42

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

Greatest Common Factor

We found the factors and prime factorization of 42 and 45. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 45 is 3.

Also check out the Least Common Multiple of 42 and 45

Properties of GCF 42 and 45

(i) The GCF of 42 and 45 is associative

GCF of 42 and 45 = GCF of 45 and 42

Related Greatest Common Factor of 42

Related Greatest Common Factor of 45

Frequently Asked Questions on GCF of 42 and 45

1. What is the GCF of 42 and 45?

Answer: GCF of 42 and 45 is 3.

2. What are the Factors of 42?

Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.

3. What are the Factors of 45?

Answer: Factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 integers that are factors of 45. The greatest factor of 45 is 45.

4. How to Find the GCF of 42 and 45?

Answer:

Greatest Common Factor of 42 and 45 = 3

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 45

45 = 3 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 = 3

Step 4: Therefore, the greatest common factor of 42 and 45 is 3