What is the Greatest Common Factor of 31314 and 31320?

Greatest common factor (GCF) of 31314 and 31320 is 6.

GCF(31314,31320) = 6

We will now calculate the prime factors of 31314 and 31320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31314 and 31320.

How to find the GCF of 31314 and 31320?

We will first find the prime factorization of 31314 and 31320. After we will calculate the factors of 31314 and 31320 and find the biggest common factor number .

Step-1: Prime Factorization of 31314

Prime factors of 31314 are 2, 3, 17, 307. Prime factorization of 31314 in exponential form is:

31314 = 2¹ × 3¹ × 17¹ × 307¹

Step-2: 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-3: Factors of 31314

List of positive integer factors of 31314 that divides 31314 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657

Step-4: Factors of 31320

List of positive integer factors of 31320 that divides 31314 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31314 and 31320. The biggest common factor number is the GCF number.
So the greatest common factor 31314 and 31320 is 6.

Also check out the Least Common Multiple of 31314 and 31320