What is the Greatest Common Factor of 74500 and 74520?

Greatest common factor (GCF) of 74500 and 74520 is 20.

GCF(74500,74520) = 20

We will now calculate the prime factors of 74500 and 74520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74500 and 74520.

How to find the GCF of 74500 and 74520?

We will first find the prime factorization of 74500 and 74520. After we will calculate the factors of 74500 and 74520 and find the biggest common factor number .

Step-1: Prime Factorization of 74500

Prime factors of 74500 are 2, 5, 149. Prime factorization of 74500 in exponential form is:

74500 = 2² × 5³ × 149¹

Step-2: Prime Factorization of 74520

Prime factors of 74520 are 2, 3, 5, 23. Prime factorization of 74520 in exponential form is:

74520 = 2³ × 3⁴ × 5¹ × 23¹

Step-3: Factors of 74500

List of positive integer factors of 74500 that divides 74500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 149, 250, 298, 500, 596, 745, 1490, 2980, 3725, 7450, 14900, 18625, 37250

Step-4: Factors of 74520

List of positive integer factors of 74520 that divides 74500 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 23, 24, 27, 30, 36, 40, 45, 46, 54, 60, 69, 72, 81, 90, 92, 108, 115, 120, 135, 138, 162, 180, 184, 207, 216, 230, 270, 276, 324, 345, 360, 405, 414, 460, 540, 552, 621, 648, 690, 810, 828, 920, 1035, 1080, 1242, 1380, 1620, 1656, 1863, 2070, 2484, 2760, 3105, 3240, 3726, 4140, 4968, 6210, 7452, 8280, 9315, 12420, 14904, 18630, 24840, 37260

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74500 and 74520. The biggest common factor number is the GCF number.
So the greatest common factor 74500 and 74520 is 20.

Also check out the Least Common Multiple of 74500 and 74520