What is the Greatest Common Factor of 74997 and 75012?

Greatest common factor (GCF) of 74997 and 75012 is 3.

GCF(74997,75012) = 3

We will now calculate the prime factors of 74997 and 75012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74997 and 75012.

How to find the GCF of 74997 and 75012?

We will first find the prime factorization of 74997 and 75012. After we will calculate the factors of 74997 and 75012 and find the biggest common factor number .

Step-1: Prime Factorization of 74997

Prime factors of 74997 are 3, 13, 641. Prime factorization of 74997 in exponential form is:

74997 = 3² × 13¹ × 641¹

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 74997

List of positive integer factors of 74997 that divides 74997 without a remainder.

1, 3, 9, 13, 39, 117, 641, 1923, 5769, 8333, 24999

Step-4: Factors of 75012

List of positive integer factors of 75012 that divides 74997 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 74997 and 75012. The biggest common factor number is the GCF number.
So the greatest common factor 74997 and 75012 is 3.

Also check out the Least Common Multiple of 74997 and 75012