What is the Greatest Common Factor of 7000 and 7014?

Greatest common factor (GCF) of 7000 and 7014 is 14.

GCF(7000,7014) = 14

We will now calculate the prime factors of 7000 and 7014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7000 and 7014.

How to find the GCF of 7000 and 7014?

We will first find the prime factorization of 7000 and 7014. After we will calculate the factors of 7000 and 7014 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 7014

Prime factors of 7014 are 2, 3, 7, 167. Prime factorization of 7014 in exponential form is:

7014 = 2¹ × 3¹ × 7¹ × 167¹

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 7014

List of positive integer factors of 7014 that divides 7000 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 167, 334, 501, 1002, 1169, 2338, 3507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7000 and 7014. The biggest common factor number is the GCF number.
So the greatest common factor 7000 and 7014 is 14.

Also check out the Least Common Multiple of 7000 and 7014