What is the Greatest Common Factor of 89980 and 90000?

Greatest common factor (GCF) of 89980 and 90000 is 20.

GCF(89980,90000) = 20

We will now calculate the prime factors of 89980 and 90000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89980 and 90000.

How to find the GCF of 89980 and 90000?

We will first find the prime factorization of 89980 and 90000. After we will calculate the factors of 89980 and 90000 and find the biggest common factor number .

Step-1: Prime Factorization of 89980

Prime factors of 89980 are 2, 5, 11, 409. Prime factorization of 89980 in exponential form is:

89980 = 2² × 5¹ × 11¹ × 409¹

Step-2: Prime Factorization of 90000

Prime factors of 90000 are 2, 3, 5. Prime factorization of 90000 in exponential form is:

90000 = 2⁴ × 3² × 5⁴

Step-3: Factors of 89980

List of positive integer factors of 89980 that divides 89980 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220, 409, 818, 1636, 2045, 4090, 4499, 8180, 8998, 17996, 22495, 44990

Step-4: Factors of 90000

List of positive integer factors of 90000 that divides 89980 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 125, 144, 150, 180, 200, 225, 240, 250, 300, 360, 375, 400, 450, 500, 600, 625, 720, 750, 900, 1000, 1125, 1200, 1250, 1500, 1800, 1875, 2000, 2250, 2500, 3000, 3600, 3750, 4500, 5000, 5625, 6000, 7500, 9000, 10000, 11250, 15000, 18000, 22500, 30000, 45000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 89980 and 90000. The biggest common factor number is the GCF number.
So the greatest common factor 89980 and 90000 is 20.

Also check out the Least Common Multiple of 89980 and 90000