Greatest Common Factor of 6174 and 6180

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 6174, 6180 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 6174 and 6180 is 6.

GCF(6174,6180) = 6

GCF of 6174 and 6180

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

GCF of:
and

Greatest Common Factor of 6174 and 6180

GCF of 6174 and 6180 is 6

Prime Factorization of 6174


2 6174
3 3087
3 1029
7 343
7 49
7 7
1

Prime factors of 6174 are 2,3,7. Prime factorization of 6174 in exponential form is:

6174 = 21×32×73

Prime Factorization of 6180


2 6180
2 3090
3 1545
5 515
103 103
1

Prime factors of 6180 are 2,3,5,103. Prime factorization of 6180 in exponential form is:

6180 = 22×31×51×1031

∴ So by taking common prime factors GCF of 6174 and 6180 is 6

Greatest Common Factor of 6174 and 6180 by matching factors method

Factors of 6174

List of positive integer factors of 6174 that divides 6174 without a remainder.

1,2,3,6,7,9,14,18,21,42,49,63,98,126,147,294,343,441,686,882,1029,2058,3087,6174

Factors of 6180

List of positive integer factors of 6180 that divides 6180 without a remainder.

1,2,3,4,5,6,10,12,15,20,30,60,103,206,309,412,515,618,1030,1236,1545,2060,3090,6180

Greatest Common Factor

We found the factors and prime factorization of 6174 and 6180. The biggest common factor number is the GCF number.
So the greatest common factor 6174 and 6180 is 6.

Also check out the Least Common Multiple of 6174 and 6180

Properties of GCF 6174 and 6180

(i) The GCF of 6174 and 6180 is associative

GCF of 6174 and 6180 = GCF of 6180 and 6174

Related Greatest Common Factor of 6174

Related Greatest Common Factor of 6180

Frequently Asked Questions on GCF of 6174 and 6180

1. What is the GCF of 6174 and 6180?

Answer: GCF of 6174 and 6180 is 6.

2. What are the Factors of 6174?

Answer: Factors of 6174 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1029, 2058, 3087, 6174. There are 24 integers that are factors of 6174. The greatest factor of 6174 is 6174.

3. What are the Factors of 6180?

Answer: Factors of 6180 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 103, 206, 309, 412, 515, 618, 1030, 1236, 1545, 2060, 3090, 6180. There are 24 integers that are factors of 6180. The greatest factor of 6180 is 6180.

4. How to Find the GCF of 6174 and 6180?

Answer:

Greatest Common Factor of 6174 and 6180 = 6

Step 1: Find the prime factorization of 6174

6174 = 2 x 3 x 3 x 7 x 7 x 7

Step 2: Find the prime factorization of 6180

6180 = 2 x 2 x 3 x 5 x 103

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 6174 and 6180 is 6