What is the Greatest Common Factor of 240 and 259?

Greatest common factor (GCF) of 240 and 259 is 1.

GCF(240,259) = 1

We will now calculate the prime factors of 240 and 259, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 240 and 259.

How to find the GCF of 240 and 259?

We will first find the prime factorization of 240 and 259. After we will calculate the factors of 240 and 259 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 259

Prime factors of 259 are 7, 37. Prime factorization of 259 in exponential form is:

259 = 7¹ × 37¹

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 259

List of positive integer factors of 259 that divides 240 without a remainder.

1, 7, 37

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 240 and 259. The biggest common factor number is the GCF number.
So the greatest common factor 240 and 259 is 1.

Also check out the Least Common Multiple of 240 and 259