What is the Greatest Common Factor of 20256 and 20272?

Greatest common factor (GCF) of 20256 and 20272 is 16.

GCF(20256,20272) = 16

We will now calculate the prime factors of 20256 and 20272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20256 and 20272.

How to find the GCF of 20256 and 20272?

We will first find the prime factorization of 20256 and 20272. After we will calculate the factors of 20256 and 20272 and find the biggest common factor number .

Step-1: Prime Factorization of 20256

Prime factors of 20256 are 2, 3, 211. Prime factorization of 20256 in exponential form is:

20256 = 2⁵ × 3¹ × 211¹

Step-2: Prime Factorization of 20272

Prime factors of 20272 are 2, 7, 181. Prime factorization of 20272 in exponential form is:

20272 = 2⁴ × 7¹ × 181¹

Step-3: Factors of 20256

List of positive integer factors of 20256 that divides 20256 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 211, 422, 633, 844, 1266, 1688, 2532, 3376, 5064, 6752, 10128

Step-4: Factors of 20272

List of positive integer factors of 20272 that divides 20256 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 181, 362, 724, 1267, 1448, 2534, 2896, 5068, 10136

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20256 and 20272. The biggest common factor number is the GCF number.
So the greatest common factor 20256 and 20272 is 16.

Also check out the Least Common Multiple of 20256 and 20272