What is the Greatest Common Factor of 7000 and 7007?

Greatest common factor (GCF) of 7000 and 7007 is 7.

GCF(7000,7007) = 7

We will now calculate the prime factors of 7000 and 7007, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7000 and 7007.

How to find the GCF of 7000 and 7007?

We will first find the prime factorization of 7000 and 7007. After we will calculate the factors of 7000 and 7007 and find the biggest common factor number .

Step-1: Prime Factorization of 7000

Prime factors of 7000 are 2, 5, 7. Prime factorization of 7000 in exponential form is:

7000 = 2³ × 5³ × 7¹

Step-2: Prime Factorization of 7007

Prime factors of 7007 are 7, 11, 13. Prime factorization of 7007 in exponential form is:

7007 = 7² × 11¹ × 13¹

Step-3: Factors of 7000

List of positive integer factors of 7000 that divides 7000 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500

Step-4: Factors of 7007

List of positive integer factors of 7007 that divides 7000 without a remainder.

1, 7, 11, 13, 49, 77, 91, 143, 539, 637, 1001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7000 and 7007. The biggest common factor number is the GCF number.
So the greatest common factor 7000 and 7007 is 7.

Also check out the Least Common Multiple of 7000 and 7007