What is the Greatest Common Factor of 75000 and 75004?

Greatest common factor (GCF) of 75000 and 75004 is 4.

GCF(75000,75004) = 4

We will now calculate the prime factors of 75000 and 75004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75000 and 75004.

How to find the GCF of 75000 and 75004?

We will first find the prime factorization of 75000 and 75004. After we will calculate the factors of 75000 and 75004 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75004

Prime factors of 75004 are 2, 17, 1103. Prime factorization of 75004 in exponential form is:

75004 = 2² × 17¹ × 1103¹

Step-3: Factors of 75000

List of positive integer factors of 75000 that divides 75000 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

Step-4: Factors of 75004

List of positive integer factors of 75004 that divides 75000 without a remainder.

1, 2, 4, 17, 34, 68, 1103, 2206, 4412, 18751, 37502

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75000 and 75004. The biggest common factor number is the GCF number.
So the greatest common factor 75000 and 75004 is 4.

Also check out the Least Common Multiple of 75000 and 75004