What is the Greatest Common Factor of 74700 and 74720?

Greatest common factor (GCF) of 74700 and 74720 is 20.

GCF(74700,74720) = 20

We will now calculate the prime factors of 74700 and 74720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74700 and 74720.

How to find the GCF of 74700 and 74720?

We will first find the prime factorization of 74700 and 74720. After we will calculate the factors of 74700 and 74720 and find the biggest common factor number .

Step-1: Prime Factorization of 74700

Prime factors of 74700 are 2, 3, 5, 83. Prime factorization of 74700 in exponential form is:

74700 = 2² × 3² × 5² × 83¹

Step-2: Prime Factorization of 74720

Prime factors of 74720 are 2, 5, 467. Prime factorization of 74720 in exponential form is:

74720 = 2⁵ × 5¹ × 467¹

Step-3: Factors of 74700

List of positive integer factors of 74700 that divides 74700 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 83, 90, 100, 150, 166, 180, 225, 249, 300, 332, 415, 450, 498, 747, 830, 900, 996, 1245, 1494, 1660, 2075, 2490, 2988, 3735, 4150, 4980, 6225, 7470, 8300, 12450, 14940, 18675, 24900, 37350

Step-4: Factors of 74720

List of positive integer factors of 74720 that divides 74700 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 467, 934, 1868, 2335, 3736, 4670, 7472, 9340, 14944, 18680, 37360

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74700 and 74720. The biggest common factor number is the GCF number.
So the greatest common factor 74700 and 74720 is 20.

Also check out the Least Common Multiple of 74700 and 74720