What is the Greatest Common Factor of 39648 and 39657?

Greatest common factor (GCF) of 39648 and 39657 is 3.

GCF(39648,39657) = 3

We will now calculate the prime factors of 39648 and 39657, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39648 and 39657.

How to find the GCF of 39648 and 39657?

We will first find the prime factorization of 39648 and 39657. After we will calculate the factors of 39648 and 39657 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 39657

Prime factors of 39657 are 3, 13219. Prime factorization of 39657 in exponential form is:

39657 = 3¹ × 13219¹

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 39657

List of positive integer factors of 39657 that divides 39648 without a remainder.

1, 3, 13219

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39648 and 39657. The biggest common factor number is the GCF number.
So the greatest common factor 39648 and 39657 is 3.

Also check out the Least Common Multiple of 39648 and 39657