What is the Greatest Common Factor of 39264 and 39270?

Greatest common factor (GCF) of 39264 and 39270 is 6.

GCF(39264,39270) = 6

We will now calculate the prime factors of 39264 and 39270, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39264 and 39270.

How to find the GCF of 39264 and 39270?

We will first find the prime factorization of 39264 and 39270. After we will calculate the factors of 39264 and 39270 and find the biggest common factor number .

Step-1: Prime Factorization of 39264

Prime factors of 39264 are 2, 3, 409. Prime factorization of 39264 in exponential form is:

39264 = 2⁵ × 3¹ × 409¹

Step-2: 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-3: Factors of 39264

List of positive integer factors of 39264 that divides 39264 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 409, 818, 1227, 1636, 2454, 3272, 4908, 6544, 9816, 13088, 19632

Step-4: Factors of 39270

List of positive integer factors of 39270 that divides 39264 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39264 and 39270. The biggest common factor number is the GCF number.
So the greatest common factor 39264 and 39270 is 6.

Also check out the Least Common Multiple of 39264 and 39270