What is the Greatest Common Factor of 39270 and 39285?

Greatest common factor (GCF) of 39270 and 39285 is 15.

GCF(39270,39285) = 15

We will now calculate the prime factors of 39270 and 39285, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39270 and 39285.

How to find the GCF of 39270 and 39285?

We will first find the prime factorization of 39270 and 39285. After we will calculate the factors of 39270 and 39285 and find the biggest common factor number .

Step-1: Prime Factorization of 39270

Prime factors of 39270 are 2, 3, 5, 7, 11, 17. Prime factorization of 39270 in exponential form is:

39270 = 2¹ × 3¹ × 5¹ × 7¹ × 11¹ × 17¹

Step-2: Prime Factorization of 39285

Prime factors of 39285 are 3, 5, 97. Prime factorization of 39285 in exponential form is:

39285 = 3⁴ × 5¹ × 97¹

Step-3: Factors of 39270

List of positive integer factors of 39270 that divides 39270 without a remainder.

1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 17, 21, 22, 30, 33, 34, 35, 42, 51, 55, 66, 70, 77, 85, 102, 105, 110, 119, 154, 165, 170, 187, 210, 231, 238, 255, 330, 357, 374, 385, 462, 510, 561, 595, 714, 770, 935, 1122, 1155, 1190, 1309, 1785, 1870, 2310, 2618, 2805, 3570, 3927, 5610, 6545, 7854, 13090, 19635

Step-4: Factors of 39285

List of positive integer factors of 39285 that divides 39270 without a remainder.

1, 3, 5, 9, 15, 27, 45, 81, 97, 135, 291, 405, 485, 873, 1455, 2619, 4365, 7857, 13095

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39270 and 39285. The biggest common factor number is the GCF number.
So the greatest common factor 39270 and 39285 is 15.

Also check out the Least Common Multiple of 39270 and 39285