Greatest Common Factor of 69 and 75

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 69, 75 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 69 and 75 is 3.

GCF(69,75) = 3

GCF of 69 and 75

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

GCF of:
and

Greatest Common Factor of 69 and 75

GCF of 69 and 75 is 3

Prime Factorization of 69


3 69
23 23
1

Prime factors of 69 are 3,23. Prime factorization of 69 in exponential form is:

69 = 31×231

Prime Factorization of 75


3 75
5 25
5 5
1

Prime factors of 75 are 3,5. Prime factorization of 75 in exponential form is:

75 = 31×52

∴ So by taking common prime factors GCF of 69 and 75 is 3

Greatest Common Factor of 69 and 75 by matching factors method

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1,3,23,69

Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

Greatest Common Factor

We found the factors and prime factorization of 69 and 75. The biggest common factor number is the GCF number.
So the greatest common factor 69 and 75 is 3.

Also check out the Least Common Multiple of 69 and 75

Properties of GCF 69 and 75

(i) The GCF of 69 and 75 is associative

GCF of 69 and 75 = GCF of 75 and 69

Related Greatest Common Factor of 69

Related Greatest Common Factor of 75

Frequently Asked Questions on GCF of 69 and 75

1. What is the GCF of 69 and 75?

Answer: GCF of 69 and 75 is 3.

2. What are the Factors of 69?

Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.

3. What are the Factors of 75?

Answer: Factors of 75 are 1, 3, 5, 15, 25, 75. There are 6 integers that are factors of 75. The greatest factor of 75 is 75.

4. How to Find the GCF of 69 and 75?

Answer:

Greatest Common Factor of 69 and 75 = 3

Step 1: Find the prime factorization of 69

69 = 3 x 23

Step 2: Find the prime factorization of 75

75 = 3 x 5 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 69 and 75 is 3