Greatest Common Factor of 68 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 68, 75 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 68 and 75 is 1.

GCF(68,75) = 1

GCF of 68 and 75

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

GCF of:
and

Greatest Common Factor of 68 and 75

GCF of 68 and 75 is 1

Prime Factorization of 68


2 68
2 34
17 17
1

Prime factors of 68 are 2,17. Prime factorization of 68 in exponential form is:

68 = 22×171

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 68 and 75 is 1

Greatest Common Factor of 68 and 75 by matching factors method

Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1,2,4,17,34,68

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 68 and 75. The biggest common factor number is the GCF number.
So the greatest common factor 68 and 75 is 1.

Also check out the Least Common Multiple of 68 and 75

Properties of GCF 68 and 75

(i) The GCF of 68 and 75 is associative

GCF of 68 and 75 = GCF of 75 and 68

Related Greatest Common Factor of 68

Related Greatest Common Factor of 75

Frequently Asked Questions on GCF of 68 and 75

1. What is the GCF of 68 and 75?

Answer: GCF of 68 and 75 is 1.

2. What are the Factors of 68?

Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.

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 68 and 75?

Answer:

Greatest Common Factor of 68 and 75 = 1

Step 1: Find the prime factorization of 68

68 = 2 x 2 x 17

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 = = 1

Step 4: Therefore, the greatest common factor of 68 and 75 is 1