What is the Greatest Common Factor of 31320 and 31328?

Greatest common factor (GCF) of 31320 and 31328 is 8.

GCF(31320,31328) = 8

We will now calculate the prime factors of 31320 and 31328, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31320 and 31328.

How to find the GCF of 31320 and 31328?

We will first find the prime factorization of 31320 and 31328. After we will calculate the factors of 31320 and 31328 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 31328

Prime factors of 31328 are 2, 11, 89. Prime factorization of 31328 in exponential form is:

31328 = 2⁵ × 11¹ × 89¹

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 31328

List of positive integer factors of 31328 that divides 31320 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 89, 176, 178, 352, 356, 712, 979, 1424, 1958, 2848, 3916, 7832, 15664

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31320 and 31328. The biggest common factor number is the GCF number.
So the greatest common factor 31320 and 31328 is 8.

Also check out the Least Common Multiple of 31320 and 31328