What is the Greatest Common Factor of 19872 and 19884?

Greatest common factor (GCF) of 19872 and 19884 is 12.

GCF(19872,19884) = 12

We will now calculate the prime factors of 19872 and 19884, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19872 and 19884.

How to find the GCF of 19872 and 19884?

We will first find the prime factorization of 19872 and 19884. After we will calculate the factors of 19872 and 19884 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 19884

Prime factors of 19884 are 2, 3, 1657. Prime factorization of 19884 in exponential form is:

19884 = 2² × 3¹ × 1657¹

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 19884

List of positive integer factors of 19884 that divides 19872 without a remainder.

1, 2, 3, 4, 6, 12, 1657, 3314, 4971, 6628, 9942

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19872 and 19884. The biggest common factor number is the GCF number.
So the greatest common factor 19872 and 19884 is 12.

Also check out the Least Common Multiple of 19872 and 19884