What is the Greatest Common Factor of 31905 and 31923?

Greatest common factor (GCF) of 31905 and 31923 is 9.

GCF(31905,31923) = 9

We will now calculate the prime factors of 31905 and 31923, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31905 and 31923.

How to find the GCF of 31905 and 31923?

We will first find the prime factorization of 31905 and 31923. After we will calculate the factors of 31905 and 31923 and find the biggest common factor number .

Step-1: Prime Factorization of 31905

Prime factors of 31905 are 3, 5, 709. Prime factorization of 31905 in exponential form is:

31905 = 3² × 5¹ × 709¹

Step-2: Prime Factorization of 31923

Prime factors of 31923 are 3, 3547. Prime factorization of 31923 in exponential form is:

31923 = 3² × 3547¹

Step-3: Factors of 31905

List of positive integer factors of 31905 that divides 31905 without a remainder.

1, 3, 5, 9, 15, 45, 709, 2127, 3545, 6381, 10635

Step-4: Factors of 31923

List of positive integer factors of 31923 that divides 31905 without a remainder.

1, 3, 9, 3547, 10641

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31905 and 31923. The biggest common factor number is the GCF number.
So the greatest common factor 31905 and 31923 is 9.

Also check out the Least Common Multiple of 31905 and 31923