What is the Greatest Common Factor of 31809 and 31815?

Greatest common factor (GCF) of 31809 and 31815 is 3.

GCF(31809,31815) = 3

We will now calculate the prime factors of 31809 and 31815, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31809 and 31815.

How to find the GCF of 31809 and 31815?

We will first find the prime factorization of 31809 and 31815. After we will calculate the factors of 31809 and 31815 and find the biggest common factor number .

Step-1: Prime Factorization of 31809

Prime factors of 31809 are 3, 23, 461. Prime factorization of 31809 in exponential form is:

31809 = 3¹ × 23¹ × 461¹

Step-2: Prime Factorization of 31815

Prime factors of 31815 are 3, 5, 7, 101. Prime factorization of 31815 in exponential form is:

31815 = 3² × 5¹ × 7¹ × 101¹

Step-3: Factors of 31809

List of positive integer factors of 31809 that divides 31809 without a remainder.

1, 3, 23, 69, 461, 1383, 10603

Step-4: Factors of 31815

List of positive integer factors of 31815 that divides 31809 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 101, 105, 303, 315, 505, 707, 909, 1515, 2121, 3535, 4545, 6363, 10605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31809 and 31815. The biggest common factor number is the GCF number.
So the greatest common factor 31809 and 31815 is 3.

Also check out the Least Common Multiple of 31809 and 31815