What is the Greatest Common Factor of 31320 and 31335?

Greatest common factor (GCF) of 31320 and 31335 is 15.

GCF(31320,31335) = 15

We will now calculate the prime factors of 31320 and 31335, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31320 and 31335.

How to find the GCF of 31320 and 31335?

We will first find the prime factorization of 31320 and 31335. After we will calculate the factors of 31320 and 31335 and find the biggest common factor number .

Step-1: Prime Factorization of 31320

Prime factors of 31320 are 2, 3, 5, 29. Prime factorization of 31320 in exponential form is:

31320 = 2³ × 3³ × 5¹ × 29¹

Step-2: Prime Factorization of 31335

Prime factors of 31335 are 3, 5, 2089. Prime factorization of 31335 in exponential form is:

31335 = 3¹ × 5¹ × 2089¹

Step-3: Factors of 31320

List of positive integer factors of 31320 that divides 31320 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 29, 30, 36, 40, 45, 54, 58, 60, 72, 87, 90, 108, 116, 120, 135, 145, 174, 180, 216, 232, 261, 270, 290, 348, 360, 435, 522, 540, 580, 696, 783, 870, 1044, 1080, 1160, 1305, 1566, 1740, 2088, 2610, 3132, 3480, 3915, 5220, 6264, 7830, 10440, 15660

Step-4: Factors of 31335

List of positive integer factors of 31335 that divides 31320 without a remainder.

1, 3, 5, 15, 2089, 6267, 10445

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31320 and 31335. The biggest common factor number is the GCF number.
So the greatest common factor 31320 and 31335 is 15.

Also check out the Least Common Multiple of 31320 and 31335