What is the Greatest Common Factor of 70000 and 70020?

Greatest common factor (GCF) of 70000 and 70020 is 20.

GCF(70000,70020) = 20

We will now calculate the prime factors of 70000 and 70020, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70000 and 70020.

How to find the GCF of 70000 and 70020?

We will first find the prime factorization of 70000 and 70020. After we will calculate the factors of 70000 and 70020 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 70020

Prime factors of 70020 are 2, 3, 5, 389. Prime factorization of 70020 in exponential form is:

70020 = 2² × 3² × 5¹ × 389¹

Step-3: Factors of 70000

List of positive integer factors of 70000 that divides 70000 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

Step-4: Factors of 70020

List of positive integer factors of 70020 that divides 70000 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 389, 778, 1167, 1556, 1945, 2334, 3501, 3890, 4668, 5835, 7002, 7780, 11670, 14004, 17505, 23340, 35010

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 70000 and 70020. The biggest common factor number is the GCF number.
So the greatest common factor 70000 and 70020 is 20.

Also check out the Least Common Multiple of 70000 and 70020