What is the Greatest Common Factor of 30475 and 30480?

Greatest common factor (GCF) of 30475 and 30480 is 5.

GCF(30475,30480) = 5

We will now calculate the prime factors of 30475 and 30480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30475 and 30480.

How to find the GCF of 30475 and 30480?

We will first find the prime factorization of 30475 and 30480. After we will calculate the factors of 30475 and 30480 and find the biggest common factor number .

Step-1: Prime Factorization of 30475

Prime factors of 30475 are 5, 23, 53. Prime factorization of 30475 in exponential form is:

30475 = 5² × 23¹ × 53¹

Step-2: Prime Factorization of 30480

Prime factors of 30480 are 2, 3, 5, 127. Prime factorization of 30480 in exponential form is:

30480 = 2⁴ × 3¹ × 5¹ × 127¹

Step-3: Factors of 30475

List of positive integer factors of 30475 that divides 30475 without a remainder.

1, 5, 23, 25, 53, 115, 265, 575, 1219, 1325, 6095

Step-4: Factors of 30480

List of positive integer factors of 30480 that divides 30475 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 127, 240, 254, 381, 508, 635, 762, 1016, 1270, 1524, 1905, 2032, 2540, 3048, 3810, 5080, 6096, 7620, 10160, 15240

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30475 and 30480. The biggest common factor number is the GCF number.
So the greatest common factor 30475 and 30480 is 5.

Also check out the Least Common Multiple of 30475 and 30480