What is the Greatest Common Factor of 39225 and 39240?

Greatest common factor (GCF) of 39225 and 39240 is 15.

GCF(39225,39240) = 15

We will now calculate the prime factors of 39225 and 39240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39225 and 39240.

How to find the GCF of 39225 and 39240?

We will first find the prime factorization of 39225 and 39240. After we will calculate the factors of 39225 and 39240 and find the biggest common factor number .

Step-1: Prime Factorization of 39225

Prime factors of 39225 are 3, 5, 523. Prime factorization of 39225 in exponential form is:

39225 = 3¹ × 5² × 523¹

Step-2: Prime Factorization of 39240

Prime factors of 39240 are 2, 3, 5, 109. Prime factorization of 39240 in exponential form is:

39240 = 2³ × 3² × 5¹ × 109¹

Step-3: Factors of 39225

List of positive integer factors of 39225 that divides 39225 without a remainder.

1, 3, 5, 15, 25, 75, 523, 1569, 2615, 7845, 13075

Step-4: Factors of 39240

List of positive integer factors of 39240 that divides 39225 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 109, 120, 180, 218, 327, 360, 436, 545, 654, 872, 981, 1090, 1308, 1635, 1962, 2180, 2616, 3270, 3924, 4360, 4905, 6540, 7848, 9810, 13080, 19620

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39225 and 39240. The biggest common factor number is the GCF number.
So the greatest common factor 39225 and 39240 is 15.

Also check out the Least Common Multiple of 39225 and 39240