What is the Greatest Common Factor of 74998 and 75012?

Greatest common factor (GCF) of 74998 and 75012 is 14.

GCF(74998,75012) = 14

We will now calculate the prime factors of 74998 and 75012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74998 and 75012.

How to find the GCF of 74998 and 75012?

We will first find the prime factorization of 74998 and 75012. After we will calculate the factors of 74998 and 75012 and find the biggest common factor number .

Step-1: Prime Factorization of 74998

Prime factors of 74998 are 2, 7, 11, 487. Prime factorization of 74998 in exponential form is:

74998 = 2¹ × 7¹ × 11¹ × 487¹

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 74998

List of positive integer factors of 74998 that divides 74998 without a remainder.

1, 2, 7, 11, 14, 22, 77, 154, 487, 974, 3409, 5357, 6818, 10714, 37499

Step-4: Factors of 75012

List of positive integer factors of 75012 that divides 74998 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 74998 and 75012. The biggest common factor number is the GCF number.
So the greatest common factor 74998 and 75012 is 14.

Also check out the Least Common Multiple of 74998 and 75012