Greatest Common Factor of 31314 and 31320

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 31314, 31320 i.e. 6 largest integer by which both the numbers can be divided.

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

GCF(31314,31320) = 6

GCF of 31314 and 31320

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 31314 and 31320

GCF of 31314 and 31320 is 6

Prime Factorization of 31314


2 31314
3 15657
17 5219
307 307
1

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

31314 = 21×31×171×3071

Prime Factorization of 31320


2 31320
2 15660
2 7830
3 3915
3 1305
3 435
5 145
29 29
1

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

31320 = 23×33×51×291

∴ So by taking common prime factors GCF of 31314 and 31320 is 6

Greatest Common Factor of 31314 and 31320 by matching factors method

Factors of 31314

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

1,2,3,6,17,34,51,102,307,614,921,1842,5219,10438,15657,31314

Factors of 31320

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

1,2,3,4,5,6,8,9,10,12,15,18,20,24,27,29,30,36,40,45,54,58,60,72,87,90,108,116,120,135,145,174,180,216,232,261,270,290,348,360,435,522,540,580,696,783,870,1044,1080,1160,1305,1566,1740,2088,2610,3132,3480,3915,5220,6264,7830,10440,15660,31320

Greatest Common Factor

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

Properties of GCF 31314 and 31320

(i) The GCF of 31314 and 31320 is associative

GCF of 31314 and 31320 = GCF of 31320 and 31314

Related Greatest Common Factor of 31314

Related Greatest Common Factor of 31320

Frequently Asked Questions on GCF of 31314 and 31320

1. What is the GCF of 31314 and 31320?

Answer: GCF of 31314 and 31320 is 6.

2. What are the Factors of 31314?

Answer: Factors of 31314 are 1, 2, 3, 6, 17, 34, 51, 102, 307, 614, 921, 1842, 5219, 10438, 15657, 31314. There are 16 integers that are factors of 31314. The greatest factor of 31314 is 31314.

3. What are the Factors of 31320?

Answer: Factors of 31320 are 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, 31320. There are 64 integers that are factors of 31320. The greatest factor of 31320 is 31320.

4. How to Find the GCF of 31314 and 31320?

Answer:

Greatest Common Factor of 31314 and 31320 = 6

Step 1: Find the prime factorization of 31314

31314 = 2 x 3 x 17 x 307

Step 2: Find the prime factorization of 31320

31320 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 29

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 31314 and 31320 is 6