What is the Greatest Common Factor of 240 and 250?

Greatest common factor (GCF) of 240 and 250 is 10.

GCF(240,250) = 10

We will now calculate the prime factors of 240 and 250, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 240 and 250.

How to find the GCF of 240 and 250?

We will first find the prime factorization of 240 and 250. After we will calculate the factors of 240 and 250 and find the biggest common factor number .

Step-1: Prime Factorization of 240

Prime factors of 240 are 2, 3, 5. Prime factorization of 240 in exponential form is:

240 = 2⁴ × 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 240

List of positive integer factors of 240 that divides 240 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120

Step-4: Factors of 250

List of positive integer factors of 250 that divides 240 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 240 and 250. The biggest common factor number is the GCF number.
So the greatest common factor 240 and 250 is 10.

Also check out the Least Common Multiple of 240 and 250