What is the Greatest Common Factor of 30 and 250?

Greatest common factor (GCF) of 30 and 250 is 10.

GCF(30,250) = 10

We will now calculate the prime factors of 30 and 250, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30 and 250.

How to find the GCF of 30 and 250?

We will first find the prime factorization of 30 and 250. After we will calculate the factors of 30 and 250 and find the biggest common factor number .

Step-1: Prime Factorization of 30

Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:

30 = 2¹ × 3¹ × 5¹

Step-2: Prime Factorization of 250

Prime factors of 250 are 2, 5. Prime factorization of 250 in exponential form is:

250 = 2¹ × 5³

Step-3: Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15

Step-4: Factors of 250

List of positive integer factors of 250 that divides 30 without a remainder.

1, 2, 5, 10, 25, 50, 125

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30 and 250. The biggest common factor number is the GCF number.
So the greatest common factor 30 and 250 is 10.

Also check out the Least Common Multiple of 30 and 250