What is the Greatest Common Factor of 75000 and 75012?

Greatest common factor (GCF) of 75000 and 75012 is 12.

GCF(75000,75012) = 12

We will now calculate the prime factors of 75000 and 75012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75000 and 75012.

How to find the GCF of 75000 and 75012?

We will first find the prime factorization of 75000 and 75012. After we will calculate the factors of 75000 and 75012 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 75012

Prime factors of 75012 are 2, 3, 7, 19, 47. Prime factorization of 75012 in exponential form is:

75012 = 2² × 3¹ × 7¹ × 19¹ × 47¹

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 75012

List of positive integer factors of 75012 that divides 75000 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 19, 21, 28, 38, 42, 47, 57, 76, 84, 94, 114, 133, 141, 188, 228, 266, 282, 329, 399, 532, 564, 658, 798, 893, 987, 1316, 1596, 1786, 1974, 2679, 3572, 3948, 5358, 6251, 10716, 12502, 18753, 25004, 37506

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75000 and 75012. The biggest common factor number is the GCF number.
So the greatest common factor 75000 and 75012 is 12.

Also check out the Least Common Multiple of 75000 and 75012