What is the Greatest Common Factor of 31854 and 31860?

Greatest common factor (GCF) of 31854 and 31860 is 6.

GCF(31854,31860) = 6

We will now calculate the prime factors of 31854 and 31860, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31854 and 31860.

How to find the GCF of 31854 and 31860?

We will first find the prime factorization of 31854 and 31860. After we will calculate the factors of 31854 and 31860 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 31860

Prime factors of 31860 are 2, 3, 5, 59. Prime factorization of 31860 in exponential form is:

31860 = 2² × 3³ × 5¹ × 59¹

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 31860

List of positive integer factors of 31860 that divides 31854 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 59, 60, 90, 108, 118, 135, 177, 180, 236, 270, 295, 354, 531, 540, 590, 708, 885, 1062, 1180, 1593, 1770, 2124, 2655, 3186, 3540, 5310, 6372, 7965, 10620, 15930

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31854 and 31860. The biggest common factor number is the GCF number.
So the greatest common factor 31854 and 31860 is 6.

Also check out the Least Common Multiple of 31854 and 31860