Greatest Common Factor of 75 and 78

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 75, 78 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 75 and 78 is 3.

GCF(75,78) = 3

GCF of 75 and 78

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

GCF of:
and

Greatest Common Factor of 75 and 78

GCF of 75 and 78 is 3

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

Prime Factorization of 78


2 78
3 39
13 13
1

Prime factors of 78 are 2,3,13. Prime factorization of 78 in exponential form is:

78 = 21×31×131

∴ So by taking common prime factors GCF of 75 and 78 is 3

Greatest Common Factor of 75 and 78 by matching factors method

Factors of 75

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

1,3,5,15,25,75

Factors of 78

List of positive integer factors of 78 that divides 78 without a remainder.

1,2,3,6,13,26,39,78

Greatest Common Factor

We found the factors and prime factorization of 75 and 78. The biggest common factor number is the GCF number.
So the greatest common factor 75 and 78 is 3.

Also check out the Least Common Multiple of 75 and 78

Properties of GCF 75 and 78

(i) The GCF of 75 and 78 is associative

GCF of 75 and 78 = GCF of 78 and 75

Related Greatest Common Factor of 75

Related Greatest Common Factor of 78

Frequently Asked Questions on GCF of 75 and 78

1. What is the GCF of 75 and 78?

Answer: GCF of 75 and 78 is 3.

2. 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.

3. What are the Factors of 78?

Answer: Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78. There are 8 integers that are factors of 78. The greatest factor of 78 is 78.

4. How to Find the GCF of 75 and 78?

Answer:

Greatest Common Factor of 75 and 78 = 3

Step 1: Find the prime factorization of 75

75 = 3 x 5 x 5

Step 2: Find the prime factorization of 78

78 = 2 x 3 x 13

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 75 and 78 is 3