What is the Greatest Common Factor of 90000 and 90009?

Greatest common factor (GCF) of 90000 and 90009 is 9.

GCF(90000,90009) = 9

We will now calculate the prime factors of 90000 and 90009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 90000 and 90009.

How to find the GCF of 90000 and 90009?

We will first find the prime factorization of 90000 and 90009. After we will calculate the factors of 90000 and 90009 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 90009

Prime factors of 90009 are 3, 73, 137. Prime factorization of 90009 in exponential form is:

90009 = 3² × 73¹ × 137¹

Step-3: Factors of 90000

List of positive integer factors of 90000 that divides 90000 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

Step-4: Factors of 90009

List of positive integer factors of 90009 that divides 90000 without a remainder.

1, 3, 9, 73, 137, 219, 411, 657, 1233, 10001, 30003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 90000 and 90009. The biggest common factor number is the GCF number.
So the greatest common factor 90000 and 90009 is 9.

Also check out the Least Common Multiple of 90000 and 90009