What is the Greatest Common Factor of 3225 and 3240?

Greatest common factor (GCF) of 3225 and 3240 is 15.

GCF(3225,3240) = 15

We will now calculate the prime factors of 3225 and 3240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3225 and 3240.

How to find the GCF of 3225 and 3240?

We will first find the prime factorization of 3225 and 3240. After we will calculate the factors of 3225 and 3240 and find the biggest common factor number .

Step-1: Prime Factorization of 3225

Prime factors of 3225 are 3, 5, 43. Prime factorization of 3225 in exponential form is:

3225 = 3¹ × 5² × 43¹

Step-2: Prime Factorization of 3240

Prime factors of 3240 are 2, 3, 5. Prime factorization of 3240 in exponential form is:

3240 = 2³ × 3⁴ × 5¹

Step-3: Factors of 3225

List of positive integer factors of 3225 that divides 3225 without a remainder.

1, 3, 5, 15, 25, 43, 75, 129, 215, 645, 1075

Step-4: Factors of 3240

List of positive integer factors of 3240 that divides 3225 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3225 and 3240. The biggest common factor number is the GCF number.
So the greatest common factor 3225 and 3240 is 15.

Also check out the Least Common Multiple of 3225 and 3240