What is the Greatest Common Factor of 31824 and 31837?

Greatest common factor (GCF) of 31824 and 31837 is 13.

GCF(31824,31837) = 13

We will now calculate the prime factors of 31824 and 31837, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31824 and 31837.

How to find the GCF of 31824 and 31837?

We will first find the prime factorization of 31824 and 31837. After we will calculate the factors of 31824 and 31837 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31837

Prime factors of 31837 are 13, 31, 79. Prime factorization of 31837 in exponential form is:

31837 = 13¹ × 31¹ × 79¹

Step-3: Factors of 31824

List of positive integer factors of 31824 that divides 31824 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

Step-4: Factors of 31837

List of positive integer factors of 31837 that divides 31824 without a remainder.

1, 13, 31, 79, 403, 1027, 2449

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31824 and 31837. The biggest common factor number is the GCF number.
So the greatest common factor 31824 and 31837 is 13.

Also check out the Least Common Multiple of 31824 and 31837