What is the Greatest Common Factor of 39648 and 39664?

Greatest common factor (GCF) of 39648 and 39664 is 16.

GCF(39648,39664) = 16

We will now calculate the prime factors of 39648 and 39664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39648 and 39664.

How to find the GCF of 39648 and 39664?

We will first find the prime factorization of 39648 and 39664. After we will calculate the factors of 39648 and 39664 and find the biggest common factor number .

Step-1: Prime Factorization of 39648

Prime factors of 39648 are 2, 3, 7, 59. Prime factorization of 39648 in exponential form is:

39648 = 2⁵ × 3¹ × 7¹ × 59¹

Step-2: 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-3: Factors of 39648

List of positive integer factors of 39648 that divides 39648 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 59, 84, 96, 112, 118, 168, 177, 224, 236, 336, 354, 413, 472, 672, 708, 826, 944, 1239, 1416, 1652, 1888, 2478, 2832, 3304, 4956, 5664, 6608, 9912, 13216, 19824

Step-4: Factors of 39664

List of positive integer factors of 39664 that divides 39648 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39648 and 39664. The biggest common factor number is the GCF number.
So the greatest common factor 39648 and 39664 is 16.

Also check out the Least Common Multiple of 39648 and 39664