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 1006, 1008 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1006 and 1008 is 2.
GCF(1006,1008) = 2
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 1006
2 | 1006 |
503 | 503 |
1 |
Prime factors of 1006 are 2,503. Prime factorization of 1006 in exponential form is:
1006 = 21×5031
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
∴ So by taking common prime factors GCF of 1006 and 1008 is 2
Factors of 1006
List of positive integer factors of 1006 that divides 1006 without a remainder.
1,2,503,1006
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
Greatest Common Factor
We found the factors and prime factorization of 1006 and 1008. The biggest common factor number is the GCF number.
So the greatest common factor 1006 and 1008 is 2.
Also check out the Least Common Multiple of 1006 and 1008
(i) The GCF of 1006 and 1008 is associative
GCF of 1006 and 1008 = GCF of 1008 and 1006
1. What is the GCF of 1006 and 1008?
Answer: GCF of 1006 and 1008 is 2.
2. What are the Factors of 1006?
Answer: Factors of 1006 are 1, 2, 503, 1006. There are 4 integers that are factors of 1006. The greatest factor of 1006 is 1006.
3. 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.
4. How to Find the GCF of 1006 and 1008?
Answer:
Greatest Common Factor of 1006 and 1008 = 2
Step 1: Find the prime factorization of 1006
1006 = 2 x 503
Step 2: Find the prime factorization of 1008
1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2
Step 4: Therefore, the greatest common factor of 1006 and 1008 is 2