What is the Greatest Common Factor of 30075 and 30080?

Greatest common factor (GCF) of 30075 and 30080 is 5.

GCF(30075,30080) = 5

We will now calculate the prime factors of 30075 and 30080, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30075 and 30080.

How to find the GCF of 30075 and 30080?

We will first find the prime factorization of 30075 and 30080. After we will calculate the factors of 30075 and 30080 and find the biggest common factor number .

Step-1: Prime Factorization of 30075

Prime factors of 30075 are 3, 5, 401. Prime factorization of 30075 in exponential form is:

30075 = 3¹ × 5² × 401¹

Step-2: Prime Factorization of 30080

Prime factors of 30080 are 2, 5, 47. Prime factorization of 30080 in exponential form is:

30080 = 2⁷ × 5¹ × 47¹

Step-3: Factors of 30075

List of positive integer factors of 30075 that divides 30075 without a remainder.

1, 3, 5, 15, 25, 75, 401, 1203, 2005, 6015, 10025

Step-4: Factors of 30080

List of positive integer factors of 30080 that divides 30075 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 47, 64, 80, 94, 128, 160, 188, 235, 320, 376, 470, 640, 752, 940, 1504, 1880, 3008, 3760, 6016, 7520, 15040

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30075 and 30080. The biggest common factor number is the GCF number.
So the greatest common factor 30075 and 30080 is 5.

Also check out the Least Common Multiple of 30075 and 30080