What is the Greatest Common Factor of 39664 and 39672?

Greatest common factor (GCF) of 39664 and 39672 is 8.

GCF(39664,39672) = 8

We will now calculate the prime factors of 39664 and 39672, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39664 and 39672.

How to find the GCF of 39664 and 39672?

We will first find the prime factorization of 39664 and 39672. After we will calculate the factors of 39664 and 39672 and find the biggest common factor number .

Step-1: Prime Factorization of 39664

Prime factors of 39664 are 2, 37, 67. Prime factorization of 39664 in exponential form is:

39664 = 2⁴ × 37¹ × 67¹

Step-2: Prime Factorization of 39672

Prime factors of 39672 are 2, 3, 19, 29. Prime factorization of 39672 in exponential form is:

39672 = 2³ × 3² × 19¹ × 29¹

Step-3: Factors of 39664

List of positive integer factors of 39664 that divides 39664 without a remainder.

1, 2, 4, 8, 16, 37, 67, 74, 134, 148, 268, 296, 536, 592, 1072, 2479, 4958, 9916, 19832

Step-4: Factors of 39672

List of positive integer factors of 39672 that divides 39664 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 29, 36, 38, 57, 58, 72, 76, 87, 114, 116, 152, 171, 174, 228, 232, 261, 342, 348, 456, 522, 551, 684, 696, 1044, 1102, 1368, 1653, 2088, 2204, 3306, 4408, 4959, 6612, 9918, 13224, 19836

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39664 and 39672. The biggest common factor number is the GCF number.
So the greatest common factor 39664 and 39672 is 8.

Also check out the Least Common Multiple of 39664 and 39672