What is the Greatest Common Factor of 30069 and 30075?

Greatest common factor (GCF) of 30069 and 30075 is 3.

GCF(30069,30075) = 3

We will now calculate the prime factors of 30069 and 30075, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30069 and 30075.

How to find the GCF of 30069 and 30075?

We will first find the prime factorization of 30069 and 30075. After we will calculate the factors of 30069 and 30075 and find the biggest common factor number .

Step-1: Prime Factorization of 30069

Prime factors of 30069 are 3, 13, 257. Prime factorization of 30069 in exponential form is:

30069 = 3² × 13¹ × 257¹

Step-2: 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-3: Factors of 30069

List of positive integer factors of 30069 that divides 30069 without a remainder.

1, 3, 9, 13, 39, 117, 257, 771, 2313, 3341, 10023

Step-4: Factors of 30075

List of positive integer factors of 30075 that divides 30069 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30069 and 30075. The biggest common factor number is the GCF number.
So the greatest common factor 30069 and 30075 is 3.

Also check out the Least Common Multiple of 30069 and 30075