What is the Greatest Common Factor of 31674 and 31680?

Greatest common factor (GCF) of 31674 and 31680 is 6.

GCF(31674,31680) = 6

We will now calculate the prime factors of 31674 and 31680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31674 and 31680.

How to find the GCF of 31674 and 31680?

We will first find the prime factorization of 31674 and 31680. After we will calculate the factors of 31674 and 31680 and find the biggest common factor number .

Step-1: Prime Factorization of 31674

Prime factors of 31674 are 2, 3, 5279. Prime factorization of 31674 in exponential form is:

31674 = 2¹ × 3¹ × 5279¹

Step-2: Prime Factorization of 31680

Prime factors of 31680 are 2, 3, 5, 11. Prime factorization of 31680 in exponential form is:

31680 = 2⁶ × 3² × 5¹ × 11¹

Step-3: Factors of 31674

List of positive integer factors of 31674 that divides 31674 without a remainder.

1, 2, 3, 6, 5279, 10558, 15837

Step-4: Factors of 31680

List of positive integer factors of 31680 that divides 31674 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 32, 33, 36, 40, 44, 45, 48, 55, 60, 64, 66, 72, 80, 88, 90, 96, 99, 110, 120, 132, 144, 160, 165, 176, 180, 192, 198, 220, 240, 264, 288, 320, 330, 352, 360, 396, 440, 480, 495, 528, 576, 660, 704, 720, 792, 880, 960, 990, 1056, 1320, 1440, 1584, 1760, 1980, 2112, 2640, 2880, 3168, 3520, 3960, 5280, 6336, 7920, 10560, 15840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31674 and 31680. The biggest common factor number is the GCF number.
So the greatest common factor 31674 and 31680 is 6.

Also check out the Least Common Multiple of 31674 and 31680