What is the Greatest Common Factor of 31809 and 31824?

Greatest common factor (GCF) of 31809 and 31824 is 3.

GCF(31809,31824) = 3

We will now calculate the prime factors of 31809 and 31824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31809 and 31824.

How to find the GCF of 31809 and 31824?

We will first find the prime factorization of 31809 and 31824. After we will calculate the factors of 31809 and 31824 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 31824

Prime factors of 31824 are 2, 3, 13, 17. Prime factorization of 31824 in exponential form is:

31824 = 2⁴ × 3² × 13¹ × 17¹

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 31824

List of positive integer factors of 31824 that divides 31809 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 17, 18, 24, 26, 34, 36, 39, 48, 51, 52, 68, 72, 78, 102, 104, 117, 136, 144, 153, 156, 204, 208, 221, 234, 272, 306, 312, 408, 442, 468, 612, 624, 663, 816, 884, 936, 1224, 1326, 1768, 1872, 1989, 2448, 2652, 3536, 3978, 5304, 7956, 10608, 15912

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31809 and 31824. The biggest common factor number is the GCF number.
So the greatest common factor 31809 and 31824 is 3.

Also check out the Least Common Multiple of 31809 and 31824