What is the Greatest Common Factor of 32004 and 32016?

Greatest common factor (GCF) of 32004 and 32016 is 12.

GCF(32004,32016) = 12

We will now calculate the prime factors of 32004 and 32016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32004 and 32016.

How to find the GCF of 32004 and 32016?

We will first find the prime factorization of 32004 and 32016. After we will calculate the factors of 32004 and 32016 and find the biggest common factor number .

Step-1: Prime Factorization of 32004

Prime factors of 32004 are 2, 3, 7, 127. Prime factorization of 32004 in exponential form is:

32004 = 2² × 3² × 7¹ × 127¹

Step-2: Prime Factorization of 32016

Prime factors of 32016 are 2, 3, 23, 29. Prime factorization of 32016 in exponential form is:

32016 = 2⁴ × 3¹ × 23¹ × 29¹

Step-3: Factors of 32004

List of positive integer factors of 32004 that divides 32004 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 127, 252, 254, 381, 508, 762, 889, 1143, 1524, 1778, 2286, 2667, 3556, 4572, 5334, 8001, 10668, 16002

Step-4: Factors of 32016

List of positive integer factors of 32016 that divides 32004 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 29, 46, 48, 58, 69, 87, 92, 116, 138, 174, 184, 232, 276, 348, 368, 464, 552, 667, 696, 1104, 1334, 1392, 2001, 2668, 4002, 5336, 8004, 10672, 16008

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32004 and 32016. The biggest common factor number is the GCF number.
So the greatest common factor 32004 and 32016 is 12.

Also check out the Least Common Multiple of 32004 and 32016