Greatest Common Factor of 1008 and 1014

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 1008, 1014 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1008 and 1014 is 6.

GCF(1008,1014) = 6

GCF of 1008 and 1014

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

GCF of:
and

Greatest Common Factor of 1008 and 1014

GCF of 1008 and 1014 is 6

Prime Factorization of 1008


2 1008
2 504
2 252
2 126
3 63
3 21
7 7
1

Prime factors of 1008 are 2,3,7. Prime factorization of 1008 in exponential form is:

1008 = 24×32×71

Prime Factorization of 1014


2 1014
3 507
13 169
13 13
1

Prime factors of 1014 are 2,3,13. Prime factorization of 1014 in exponential form is:

1014 = 21×31×132

∴ So by taking common prime factors GCF of 1008 and 1014 is 6

Greatest Common Factor of 1008 and 1014 by matching factors method

Factors of 1008

List of positive integer factors of 1008 that divides 1008 without a remainder.

1,2,3,4,6,7,8,9,12,14,16,18,21,24,28,36,42,48,56,63,72,84,112,126,144,168,252,336,504,1008

Factors of 1014

List of positive integer factors of 1014 that divides 1014 without a remainder.

1,2,3,6,13,26,39,78,169,338,507,1014

Greatest Common Factor

We found the factors and prime factorization of 1008 and 1014. The biggest common factor number is the GCF number.
So the greatest common factor 1008 and 1014 is 6.

Also check out the Least Common Multiple of 1008 and 1014

Properties of GCF 1008 and 1014

(i) The GCF of 1008 and 1014 is associative

GCF of 1008 and 1014 = GCF of 1014 and 1008

Related Greatest Common Factor of 1008

Related Greatest Common Factor of 1014

Frequently Asked Questions on GCF of 1008 and 1014

1. What is the GCF of 1008 and 1014?

Answer: GCF of 1008 and 1014 is 6.

2. What are the Factors of 1008?

Answer: Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. There are 30 integers that are factors of 1008. The greatest factor of 1008 is 1008.

3. What are the Factors of 1014?

Answer: Factors of 1014 are 1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014. There are 12 integers that are factors of 1014. The greatest factor of 1014 is 1014.

4. How to Find the GCF of 1008 and 1014?

Answer:

Greatest Common Factor of 1008 and 1014 = 6

Step 1: Find the prime factorization of 1008

1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 1014

1014 = 2 x 3 x 13 x 13

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 1008 and 1014 is 6