What is the Greatest Common Factor of 69986 and 70000?

Greatest common factor (GCF) of 69986 and 70000 is 14.

GCF(69986,70000) = 14

We will now calculate the prime factors of 69986 and 70000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69986 and 70000.

How to find the GCF of 69986 and 70000?

We will first find the prime factorization of 69986 and 70000. After we will calculate the factors of 69986 and 70000 and find the biggest common factor number .

Step-1: Prime Factorization of 69986

Prime factors of 69986 are 2, 7, 4999. Prime factorization of 69986 in exponential form is:

69986 = 2¹ × 7¹ × 4999¹

Step-2: Prime Factorization of 70000

Prime factors of 70000 are 2, 5, 7. Prime factorization of 70000 in exponential form is:

70000 = 2⁴ × 5⁴ × 7¹

Step-3: Factors of 69986

List of positive integer factors of 69986 that divides 69986 without a remainder.

1, 2, 7, 14, 4999, 9998, 34993

Step-4: Factors of 70000

List of positive integer factors of 70000 that divides 69986 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 125, 140, 175, 200, 250, 280, 350, 400, 500, 560, 625, 700, 875, 1000, 1250, 1400, 1750, 2000, 2500, 2800, 3500, 4375, 5000, 7000, 8750, 10000, 14000, 17500, 35000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69986 and 70000. The biggest common factor number is the GCF number.
So the greatest common factor 69986 and 70000 is 14.

Also check out the Least Common Multiple of 69986 and 70000