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 3997, 4004 i.e. 7 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 3997 and 4004 is 7.
GCF(3997,4004) = 7
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 3997
7 | 3997 |
571 | 571 |
1 |
Prime factors of 3997 are 7,571. Prime factorization of 3997 in exponential form is:
3997 = 71×5711
Prime Factorization of 4004
2 | 4004 |
2 | 2002 |
7 | 1001 |
11 | 143 |
13 | 13 |
1 |
Prime factors of 4004 are 2,7,11,13. Prime factorization of 4004 in exponential form is:
4004 = 22×71×111×131
∴ So by taking common prime factors GCF of 3997 and 4004 is 7
Factors of 3997
List of positive integer factors of 3997 that divides 3997 without a remainder.
1,7,571,3997
Factors of 4004
List of positive integer factors of 4004 that divides 4004 without a remainder.
1,2,4,7,11,13,14,22,26,28,44,52,77,91,143,154,182,286,308,364,572,1001,2002,4004
Greatest Common Factor
We found the factors and prime factorization of 3997 and 4004. The biggest common factor number is the GCF number.
So the greatest common factor 3997 and 4004 is 7.
Also check out the Least Common Multiple of 3997 and 4004
(i) The GCF of 3997 and 4004 is associative
GCF of 3997 and 4004 = GCF of 4004 and 3997
1. What is the GCF of 3997 and 4004?
Answer: GCF of 3997 and 4004 is 7.
2. What are the Factors of 3997?
Answer: Factors of 3997 are 1, 7, 571, 3997. There are 4 integers that are factors of 3997. The greatest factor of 3997 is 3997.
3. What are the Factors of 4004?
Answer: Factors of 4004 are 1, 2, 4, 7, 11, 13, 14, 22, 26, 28, 44, 52, 77, 91, 143, 154, 182, 286, 308, 364, 572, 1001, 2002, 4004. There are 24 integers that are factors of 4004. The greatest factor of 4004 is 4004.
4. How to Find the GCF of 3997 and 4004?
Answer:
Greatest Common Factor of 3997 and 4004 = 7
Step 1: Find the prime factorization of 3997
3997 = 7 x 571
Step 2: Find the prime factorization of 4004
4004 = 2 x 2 x 7 x 11 x 13
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 7
Step 4: Therefore, the greatest common factor of 3997 and 4004 is 7