What is the Greatest Common Factor of 31845 and 31854?

Greatest common factor (GCF) of 31845 and 31854 is 3.

GCF(31845,31854) = 3

We will now calculate the prime factors of 31845 and 31854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31845 and 31854.

How to find the GCF of 31845 and 31854?

We will first find the prime factorization of 31845 and 31854. After we will calculate the factors of 31845 and 31854 and find the biggest common factor number .

Step-1: Prime Factorization of 31845

Prime factors of 31845 are 3, 5, 11, 193. Prime factorization of 31845 in exponential form is:

31845 = 3¹ × 5¹ × 11¹ × 193¹

Step-2: 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-3: Factors of 31845

List of positive integer factors of 31845 that divides 31845 without a remainder.

1, 3, 5, 11, 15, 33, 55, 165, 193, 579, 965, 2123, 2895, 6369, 10615

Step-4: Factors of 31854

List of positive integer factors of 31854 that divides 31845 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31845 and 31854. The biggest common factor number is the GCF number.
So the greatest common factor 31845 and 31854 is 3.

Also check out the Least Common Multiple of 31845 and 31854