What is the Greatest Common Factor of 31854 and 31872?

Greatest common factor (GCF) of 31854 and 31872 is 6.

GCF(31854,31872) = 6

We will now calculate the prime factors of 31854 and 31872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31854 and 31872.

How to find the GCF of 31854 and 31872?

We will first find the prime factorization of 31854 and 31872. After we will calculate the factors of 31854 and 31872 and find the biggest common factor number .

Step-1: Prime Factorization of 31854

Prime factors of 31854 are 2, 3, 5309. Prime factorization of 31854 in exponential form is:

31854 = 2¹ × 3¹ × 5309¹

Step-2: Prime Factorization of 31872

Prime factors of 31872 are 2, 3, 83. Prime factorization of 31872 in exponential form is:

31872 = 2⁷ × 3¹ × 83¹

Step-3: Factors of 31854

List of positive integer factors of 31854 that divides 31854 without a remainder.

1, 2, 3, 6, 5309, 10618, 15927

Step-4: Factors of 31872

List of positive integer factors of 31872 that divides 31854 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 83, 96, 128, 166, 192, 249, 332, 384, 498, 664, 996, 1328, 1992, 2656, 3984, 5312, 7968, 10624, 15936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31854 and 31872. The biggest common factor number is the GCF number.
So the greatest common factor 31854 and 31872 is 6.

Also check out the Least Common Multiple of 31854 and 31872