Greatest Common Factor of 31410 and 31416

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 31410, 31416 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 31410 and 31416 is 6.

GCF(31410,31416) = 6

GCF of 31410 and 31416

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

GCF of:
and

Greatest Common Factor of 31410 and 31416

GCF of 31410 and 31416 is 6

Prime Factorization of 31410


2 31410
3 15705
3 5235
5 1745
349 349
1

Prime factors of 31410 are 2,3,5,349. Prime factorization of 31410 in exponential form is:

31410 = 21×32×51×3491

Prime Factorization of 31416


2 31416
2 15708
2 7854
3 3927
7 1309
11 187
17 17
1

Prime factors of 31416 are 2,3,7,11,17. Prime factorization of 31416 in exponential form is:

31416 = 23×31×71×111×171

∴ So by taking common prime factors GCF of 31410 and 31416 is 6

Greatest Common Factor of 31410 and 31416 by matching factors method

Factors of 31410

List of positive integer factors of 31410 that divides 31410 without a remainder.

1,2,3,5,6,9,10,15,18,30,45,90,349,698,1047,1745,2094,3141,3490,5235,6282,10470,15705,31410

Factors of 31416

List of positive integer factors of 31416 that divides 31416 without a remainder.

1,2,3,4,6,7,8,11,12,14,17,21,22,24,28,33,34,42,44,51,56,66,68,77,84,88,102,119,132,136,154,168,187,204,231,238,264,308,357,374,408,462,476,561,616,714,748,924,952,1122,1309,1428,1496,1848,2244,2618,2856,3927,4488,5236,7854,10472,15708,31416

Greatest Common Factor

We found the factors and prime factorization of 31410 and 31416. The biggest common factor number is the GCF number.
So the greatest common factor 31410 and 31416 is 6.

Also check out the Least Common Multiple of 31410 and 31416

Properties of GCF 31410 and 31416

(i) The GCF of 31410 and 31416 is associative

GCF of 31410 and 31416 = GCF of 31416 and 31410

Related Greatest Common Factor of 31410

Related Greatest Common Factor of 31416

Frequently Asked Questions on GCF of 31410 and 31416

1. What is the GCF of 31410 and 31416?

Answer: GCF of 31410 and 31416 is 6.

2. What are the Factors of 31410?

Answer: Factors of 31410 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 349, 698, 1047, 1745, 2094, 3141, 3490, 5235, 6282, 10470, 15705, 31410. There are 24 integers that are factors of 31410. The greatest factor of 31410 is 31410.

3. What are the Factors of 31416?

Answer: Factors of 31416 are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 17, 21, 22, 24, 28, 33, 34, 42, 44, 51, 56, 66, 68, 77, 84, 88, 102, 119, 132, 136, 154, 168, 187, 204, 231, 238, 264, 308, 357, 374, 408, 462, 476, 561, 616, 714, 748, 924, 952, 1122, 1309, 1428, 1496, 1848, 2244, 2618, 2856, 3927, 4488, 5236, 7854, 10472, 15708, 31416. There are 64 integers that are factors of 31416. The greatest factor of 31416 is 31416.

4. How to Find the GCF of 31410 and 31416?

Answer:

Greatest Common Factor of 31410 and 31416 = 6

Step 1: Find the prime factorization of 31410

31410 = 2 x 3 x 3 x 5 x 349

Step 2: Find the prime factorization of 31416

31416 = 2 x 2 x 2 x 3 x 7 x 11 x 17

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 31410 and 31416 is 6