What is the Greatest Common Factor of 20000 and 20009?

Greatest common factor (GCF) of 20000 and 20009 is 1.

GCF(20000,20009) = 1

We will now calculate the prime factors of 20000 and 20009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20000 and 20009.

How to find the GCF of 20000 and 20009?

We will first find the prime factorization of 20000 and 20009. After we will calculate the factors of 20000 and 20009 and find the biggest common factor number .

Step-1: Prime Factorization of 20000

Prime factors of 20000 are 2, 5. Prime factorization of 20000 in exponential form is:

20000 = 2⁵ × 5⁴

Step-2: Prime Factorization of 20009

Prime factors of 20009 are 11, 17, 107. Prime factorization of 20009 in exponential form is:

20009 = 11¹ × 17¹ × 107¹

Step-3: Factors of 20000

List of positive integer factors of 20000 that divides 20000 without a remainder.

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

Step-4: Factors of 20009

List of positive integer factors of 20009 that divides 20000 without a remainder.

1, 11, 17, 107, 187, 1177, 1819

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20000 and 20009. The biggest common factor number is the GCF number.
So the greatest common factor 20000 and 20009 is 1.

Also check out the Least Common Multiple of 20000 and 20009