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Greatest Common Factor of 60 and 68

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 60, 68 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 60 and 68 is 4.

GCF(60,68) = 4

GCF of 60 and 68

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

GCF of:
and

Greatest Common Factor of 60 and 68 by Prime factorization method

Prime Factorization of 60


2 60
2 30
3 15
5 5
1

Prime factors of 60 are 2,3,5. Prime factorization of 60 in exponential form is:

60 = 22×31×51

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

∴ So by taking common prime factors GCF of 60 and 68 is 4

Greatest Common Factor of 60 and 68 by matching factors method

Factors of 60

List of positive integer factors of 60 that divides 60 without a remainder.

1,2,3,4,5,6,10,12,15,20,30,60

Factors of 68

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

1,2,4,17,34,68

Greatest Common Factor

We found the factors and prime factorization of 60 and 68. The biggest common factor number is the GCF number.
So the greatest common factor 60 and 68 is 4.

Also check out the Least Common Multiple of 60 and 68

Properties of GCF 60 and 68

(i) The GCF of 60 and 68 is associative

GCF of 60 and 68 = GCF of 68 and 60

Frequently Asked Questions on GCF of 60 and 68

1. What is the GCF of 60 and 68?

Answer: GCF of 60 and 68 is 4.

2. What are the Factors of 60?

Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.

3. 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.

4. How to Find the GCF of 60 and 68?

Answer:

Greatest Common Factor of 60 and 68 = 4

Step 1: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 68

68 = 2 x 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 x 2 = 4

Step 4: Therefore, the greatest common factor of 60 and 68 is 4