What is the Greatest Common Factor of 78225 and 78240?

Greatest common factor (GCF) of 78225 and 78240 is 15.

GCF(78225,78240) = 15

We will now calculate the prime factors of 78225 and 78240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78225 and 78240.

How to find the GCF of 78225 and 78240?

We will first find the prime factorization of 78225 and 78240. After we will calculate the factors of 78225 and 78240 and find the biggest common factor number .

Step-1: Prime Factorization of 78225

Prime factors of 78225 are 3, 5, 7, 149. Prime factorization of 78225 in exponential form is:

78225 = 3¹ × 5² × 7¹ × 149¹

Step-2: Prime Factorization of 78240

Prime factors of 78240 are 2, 3, 5, 163. Prime factorization of 78240 in exponential form is:

78240 = 2⁵ × 3¹ × 5¹ × 163¹

Step-3: Factors of 78225

List of positive integer factors of 78225 that divides 78225 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 149, 175, 447, 525, 745, 1043, 2235, 3129, 3725, 5215, 11175, 15645, 26075

Step-4: Factors of 78240

List of positive integer factors of 78240 that divides 78225 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 163, 240, 326, 480, 489, 652, 815, 978, 1304, 1630, 1956, 2445, 2608, 3260, 3912, 4890, 5216, 6520, 7824, 9780, 13040, 15648, 19560, 26080, 39120

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78225 and 78240. The biggest common factor number is the GCF number.
So the greatest common factor 78225 and 78240 is 15.

Also check out the Least Common Multiple of 78225 and 78240