What is the Greatest Common Factor of 31680 and 31689?

Greatest common factor (GCF) of 31680 and 31689 is 9.

GCF(31680,31689) = 9

We will now calculate the prime factors of 31680 and 31689, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31680 and 31689.

How to find the GCF of 31680 and 31689?

We will first find the prime factorization of 31680 and 31689. After we will calculate the factors of 31680 and 31689 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 31689

Prime factors of 31689 are 3, 7, 503. Prime factorization of 31689 in exponential form is:

31689 = 3² × 7¹ × 503¹

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 31689

List of positive integer factors of 31689 that divides 31680 without a remainder.

1, 3, 7, 9, 21, 63, 503, 1509, 3521, 4527, 10563

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31680 and 31689. The biggest common factor number is the GCF number.
So the greatest common factor 31680 and 31689 is 9.

Also check out the Least Common Multiple of 31680 and 31689