What is the Greatest Common Factor of 74125 and 74130?

Greatest common factor (GCF) of 74125 and 74130 is 5.

GCF(74125,74130) = 5

We will now calculate the prime factors of 74125 and 74130, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74125 and 74130.

How to find the GCF of 74125 and 74130?

We will first find the prime factorization of 74125 and 74130. After we will calculate the factors of 74125 and 74130 and find the biggest common factor number .

Step-1: Prime Factorization of 74125

Prime factors of 74125 are 5, 593. Prime factorization of 74125 in exponential form is:

74125 = 5³ × 593¹

Step-2: Prime Factorization of 74130

Prime factors of 74130 are 2, 3, 5, 7, 353. Prime factorization of 74130 in exponential form is:

74130 = 2¹ × 3¹ × 5¹ × 7¹ × 353¹

Step-3: Factors of 74125

List of positive integer factors of 74125 that divides 74125 without a remainder.

1, 5, 25, 125, 593, 2965, 14825

Step-4: Factors of 74130

List of positive integer factors of 74130 that divides 74125 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210, 353, 706, 1059, 1765, 2118, 2471, 3530, 4942, 5295, 7413, 10590, 12355, 14826, 24710, 37065

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74125 and 74130. The biggest common factor number is the GCF number.
So the greatest common factor 74125 and 74130 is 5.

Also check out the Least Common Multiple of 74125 and 74130