What is the Greatest Common Factor of 7000 and 7006?

Greatest common factor (GCF) of 7000 and 7006 is 2.

GCF(7000,7006) = 2

We will now calculate the prime factors of 7000 and 7006, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7000 and 7006.

How to find the GCF of 7000 and 7006?

We will first find the prime factorization of 7000 and 7006. After we will calculate the factors of 7000 and 7006 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 7006

Prime factors of 7006 are 2, 31, 113. Prime factorization of 7006 in exponential form is:

7006 = 2¹ × 31¹ × 113¹

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 7006

List of positive integer factors of 7006 that divides 7000 without a remainder.

1, 2, 31, 62, 113, 226, 3503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7000 and 7006. The biggest common factor number is the GCF number.
So the greatest common factor 7000 and 7006 is 2.

Also check out the Least Common Multiple of 7000 and 7006