What is the Greatest Common Factor of 75000 and 75014?

Greatest common factor (GCF) of 75000 and 75014 is 2.

GCF(75000,75014) = 2

We will now calculate the prime factors of 75000 and 75014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75000 and 75014.

How to find the GCF of 75000 and 75014?

We will first find the prime factorization of 75000 and 75014. After we will calculate the factors of 75000 and 75014 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 75014

Prime factors of 75014 are 2, 37507. Prime factorization of 75014 in exponential form is:

75014 = 2¹ × 37507¹

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 75014

List of positive integer factors of 75014 that divides 75000 without a remainder.

1, 2, 37507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75000 and 75014. The biggest common factor number is the GCF number.
So the greatest common factor 75000 and 75014 is 2.

Also check out the Least Common Multiple of 75000 and 75014