What is the Greatest Common Factor of 31680 and 31698?

Greatest common factor (GCF) of 31680 and 31698 is 18.

GCF(31680,31698) = 18

We will now calculate the prime factors of 31680 and 31698, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31680 and 31698.

How to find the GCF of 31680 and 31698?

We will first find the prime factorization of 31680 and 31698. After we will calculate the factors of 31680 and 31698 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31698

Prime factors of 31698 are 2, 3, 587. Prime factorization of 31698 in exponential form is:

31698 = 2¹ × 3³ × 587¹

Step-3: Factors of 31680

List of positive integer factors of 31680 that divides 31680 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

Step-4: Factors of 31698

List of positive integer factors of 31698 that divides 31680 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 587, 1174, 1761, 3522, 5283, 10566, 15849

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31680 and 31698. The biggest common factor number is the GCF number.
So the greatest common factor 31680 and 31698 is 18.

Also check out the Least Common Multiple of 31680 and 31698