What is the Greatest Common Factor of 74984 and 75000?

Greatest common factor (GCF) of 74984 and 75000 is 8.

GCF(74984,75000) = 8

We will now calculate the prime factors of 74984 and 75000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74984 and 75000.

How to find the GCF of 74984 and 75000?

We will first find the prime factorization of 74984 and 75000. After we will calculate the factors of 74984 and 75000 and find the biggest common factor number .

Step-1: Prime Factorization of 74984

Prime factors of 74984 are 2, 7, 13, 103. Prime factorization of 74984 in exponential form is:

74984 = 2³ × 7¹ × 13¹ × 103¹

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 74984

List of positive integer factors of 74984 that divides 74984 without a remainder.

1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 103, 104, 182, 206, 364, 412, 721, 728, 824, 1339, 1442, 2678, 2884, 5356, 5768, 9373, 10712, 18746, 37492

Step-4: Factors of 75000

List of positive integer factors of 75000 that divides 74984 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 74984 and 75000. The biggest common factor number is the GCF number.
So the greatest common factor 74984 and 75000 is 8.

Also check out the Least Common Multiple of 74984 and 75000