What is the Greatest Common Factor of 4004 and 4009?

Greatest common factor (GCF) of 4004 and 4009 is 1.

GCF(4004,4009) = 1

We will now calculate the prime factors of 4004 and 4009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4004 and 4009.

How to find the GCF of 4004 and 4009?

We will first find the prime factorization of 4004 and 4009. After we will calculate the factors of 4004 and 4009 and find the biggest common factor number .

Step-1: Prime Factorization of 4004

Prime factors of 4004 are 2, 7, 11, 13. Prime factorization of 4004 in exponential form is:

4004 = 2² × 7¹ × 11¹ × 13¹

Step-2: Prime Factorization of 4009

Prime factors of 4009 are 19, 211. Prime factorization of 4009 in exponential form is:

4009 = 19¹ × 211¹

Step-3: 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

Step-4: Factors of 4009

List of positive integer factors of 4009 that divides 4004 without a remainder.

1, 19, 211

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4004 and 4009. The biggest common factor number is the GCF number.
So the greatest common factor 4004 and 4009 is 1.

Also check out the Least Common Multiple of 4004 and 4009