What is the Greatest Common Factor of 39216 and 39225?

Greatest common factor (GCF) of 39216 and 39225 is 3.

GCF(39216,39225) = 3

We will now calculate the prime factors of 39216 and 39225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39216 and 39225.

How to find the GCF of 39216 and 39225?

We will first find the prime factorization of 39216 and 39225. After we will calculate the factors of 39216 and 39225 and find the biggest common factor number .

Step-1: Prime Factorization of 39216

Prime factors of 39216 are 2, 3, 19, 43. Prime factorization of 39216 in exponential form is:

39216 = 2⁴ × 3¹ × 19¹ × 43¹

Step-2: 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-3: Factors of 39216

List of positive integer factors of 39216 that divides 39216 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 43, 48, 57, 76, 86, 114, 129, 152, 172, 228, 258, 304, 344, 456, 516, 688, 817, 912, 1032, 1634, 2064, 2451, 3268, 4902, 6536, 9804, 13072, 19608

Step-4: Factors of 39225

List of positive integer factors of 39225 that divides 39216 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39216 and 39225. The biggest common factor number is the GCF number.
So the greatest common factor 39216 and 39225 is 3.

Also check out the Least Common Multiple of 39216 and 39225