What is the Greatest Common Factor of 40000 and 40020?

Greatest common factor (GCF) of 40000 and 40020 is 20.

GCF(40000,40020) = 20

We will now calculate the prime factors of 40000 and 40020, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 40000 and 40020.

How to find the GCF of 40000 and 40020?

We will first find the prime factorization of 40000 and 40020. After we will calculate the factors of 40000 and 40020 and find the biggest common factor number .

Step-1: Prime Factorization of 40000

Prime factors of 40000 are 2, 5. Prime factorization of 40000 in exponential form is:

40000 = 2⁶ × 5⁴

Step-2: Prime Factorization of 40020

Prime factors of 40020 are 2, 3, 5, 23, 29. Prime factorization of 40020 in exponential form is:

40020 = 2² × 3¹ × 5¹ × 23¹ × 29¹

Step-3: Factors of 40000

List of positive integer factors of 40000 that divides 40000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 625, 800, 1000, 1250, 1600, 2000, 2500, 4000, 5000, 8000, 10000, 20000

Step-4: Factors of 40020

List of positive integer factors of 40020 that divides 40000 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 29, 30, 46, 58, 60, 69, 87, 92, 115, 116, 138, 145, 174, 230, 276, 290, 345, 348, 435, 460, 580, 667, 690, 870, 1334, 1380, 1740, 2001, 2668, 3335, 4002, 6670, 8004, 10005, 13340, 20010

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 40000 and 40020. The biggest common factor number is the GCF number.
So the greatest common factor 40000 and 40020 is 20.

Also check out the Least Common Multiple of 40000 and 40020