What is the Greatest Common Factor of 74985 and 75000?

Greatest common factor (GCF) of 74985 and 75000 is 15.

GCF(74985,75000) = 15

We will now calculate the prime factors of 74985 and 75000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74985 and 75000.

How to find the GCF of 74985 and 75000?

We will first find the prime factorization of 74985 and 75000. After we will calculate the factors of 74985 and 75000 and find the biggest common factor number .

Step-1: Prime Factorization of 74985

Prime factors of 74985 are 3, 5, 4999. Prime factorization of 74985 in exponential form is:

74985 = 3¹ × 5¹ × 4999¹

Step-2: Prime Factorization of 75000

Prime factors of 75000 are 2, 3, 5. Prime factorization of 75000 in exponential form is:

75000 = 2³ × 3¹ × 5⁵

Step-3: Factors of 74985

List of positive integer factors of 74985 that divides 74985 without a remainder.

1, 3, 5, 15, 4999, 14997, 24995

Step-4: Factors of 75000

List of positive integer factors of 75000 that divides 74985 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 625, 750, 1000, 1250, 1500, 1875, 2500, 3000, 3125, 3750, 5000, 6250, 7500, 9375, 12500, 15000, 18750, 25000, 37500

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74985 and 75000. The biggest common factor number is the GCF number.
So the greatest common factor 74985 and 75000 is 15.

Also check out the Least Common Multiple of 74985 and 75000