What is the Greatest Common Factor of 74990 and 75000?

Greatest common factor (GCF) of 74990 and 75000 is 10.

GCF(74990,75000) = 10

We will now calculate the prime factors of 74990 and 75000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74990 and 75000.

How to find the GCF of 74990 and 75000?

We will first find the prime factorization of 74990 and 75000. After we will calculate the factors of 74990 and 75000 and find the biggest common factor number .

Step-1: Prime Factorization of 74990

Prime factors of 74990 are 2, 5, 7499. Prime factorization of 74990 in exponential form is:

74990 = 2¹ × 5¹ × 7499¹

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 74990

List of positive integer factors of 74990 that divides 74990 without a remainder.

1, 2, 5, 10, 7499, 14998, 37495

Step-4: Factors of 75000

List of positive integer factors of 75000 that divides 74990 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 74990 and 75000. The biggest common factor number is the GCF number.
So the greatest common factor 74990 and 75000 is 10.

Also check out the Least Common Multiple of 74990 and 75000