What is the Greatest Common Factor of 39270 and 39284?

Greatest common factor (GCF) of 39270 and 39284 is 14.

GCF(39270,39284) = 14

We will now calculate the prime factors of 39270 and 39284, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39270 and 39284.

How to find the GCF of 39270 and 39284?

We will first find the prime factorization of 39270 and 39284. After we will calculate the factors of 39270 and 39284 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 39284

Prime factors of 39284 are 2, 7, 23, 61. Prime factorization of 39284 in exponential form is:

39284 = 2² × 7¹ × 23¹ × 61¹

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 39284

List of positive integer factors of 39284 that divides 39270 without a remainder.

1, 2, 4, 7, 14, 23, 28, 46, 61, 92, 122, 161, 244, 322, 427, 644, 854, 1403, 1708, 2806, 5612, 9821, 19642

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39270 and 39284. The biggest common factor number is the GCF number.
So the greatest common factor 39270 and 39284 is 14.

Also check out the Least Common Multiple of 39270 and 39284