What is the Greatest Common Factor of 30075 and 30084?

Greatest common factor (GCF) of 30075 and 30084 is 3.

GCF(30075,30084) = 3

We will now calculate the prime factors of 30075 and 30084, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30075 and 30084.

How to find the GCF of 30075 and 30084?

We will first find the prime factorization of 30075 and 30084. After we will calculate the factors of 30075 and 30084 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 30084

Prime factors of 30084 are 2, 3, 23, 109. Prime factorization of 30084 in exponential form is:

30084 = 2² × 3¹ × 23¹ × 109¹

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 30084

List of positive integer factors of 30084 that divides 30075 without a remainder.

1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 109, 138, 218, 276, 327, 436, 654, 1308, 2507, 5014, 7521, 10028, 15042

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30075 and 30084. The biggest common factor number is the GCF number.
So the greatest common factor 30075 and 30084 is 3.

Also check out the Least Common Multiple of 30075 and 30084