What is the Greatest Common Factor of 19872 and 19888?

Greatest common factor (GCF) of 19872 and 19888 is 16.

GCF(19872,19888) = 16

We will now calculate the prime factors of 19872 and 19888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19872 and 19888.

How to find the GCF of 19872 and 19888?

We will first find the prime factorization of 19872 and 19888. After we will calculate the factors of 19872 and 19888 and find the biggest common factor number .

Step-1: Prime Factorization of 19872

Prime factors of 19872 are 2, 3, 23. Prime factorization of 19872 in exponential form is:

19872 = 2⁵ × 3³ × 23¹

Step-2: Prime Factorization of 19888

Prime factors of 19888 are 2, 11, 113. Prime factorization of 19888 in exponential form is:

19888 = 2⁴ × 11¹ × 113¹

Step-3: Factors of 19872

List of positive integer factors of 19872 that divides 19872 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 27, 32, 36, 46, 48, 54, 69, 72, 92, 96, 108, 138, 144, 184, 207, 216, 276, 288, 368, 414, 432, 552, 621, 736, 828, 864, 1104, 1242, 1656, 2208, 2484, 3312, 4968, 6624, 9936

Step-4: Factors of 19888

List of positive integer factors of 19888 that divides 19872 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 113, 176, 226, 452, 904, 1243, 1808, 2486, 4972, 9944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19872 and 19888. The biggest common factor number is the GCF number.
So the greatest common factor 19872 and 19888 is 16.

Also check out the Least Common Multiple of 19872 and 19888