Greatest Common Factor of 8208 and 8214

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 8208, 8214 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 8208 and 8214 is 6.

GCF(8208,8214) = 6

GCF of 8208 and 8214

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

GCF of:
and

Greatest Common Factor of 8208 and 8214

GCF of 8208 and 8214 is 6

Prime Factorization of 8208


2 8208
2 4104
2 2052
2 1026
3 513
3 171
3 57
19 19
1

Prime factors of 8208 are 2,3,19. Prime factorization of 8208 in exponential form is:

8208 = 24×33×191

Prime Factorization of 8214


2 8214
3 4107
37 1369
37 37
1

Prime factors of 8214 are 2,3,37. Prime factorization of 8214 in exponential form is:

8214 = 21×31×372

∴ So by taking common prime factors GCF of 8208 and 8214 is 6

Greatest Common Factor of 8208 and 8214 by matching factors method

Factors of 8208

List of positive integer factors of 8208 that divides 8208 without a remainder.

1,2,3,4,6,8,9,12,16,18,19,24,27,36,38,48,54,57,72,76,108,114,144,152,171,216,228,304,342,432,456,513,684,912,1026,1368,2052,2736,4104,8208

Factors of 8214

List of positive integer factors of 8214 that divides 8214 without a remainder.

1,2,3,6,37,74,111,222,1369,2738,4107,8214

Greatest Common Factor

We found the factors and prime factorization of 8208 and 8214. The biggest common factor number is the GCF number.
So the greatest common factor 8208 and 8214 is 6.

Also check out the Least Common Multiple of 8208 and 8214

Properties of GCF 8208 and 8214

(i) The GCF of 8208 and 8214 is associative

GCF of 8208 and 8214 = GCF of 8214 and 8208

Related Greatest Common Factor of 8208

Related Greatest Common Factor of 8214

Frequently Asked Questions on GCF of 8208 and 8214

1. What is the GCF of 8208 and 8214?

Answer: GCF of 8208 and 8214 is 6.

2. What are the Factors of 8208?

Answer: Factors of 8208 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 36, 38, 48, 54, 57, 72, 76, 108, 114, 144, 152, 171, 216, 228, 304, 342, 432, 456, 513, 684, 912, 1026, 1368, 2052, 2736, 4104, 8208. There are 40 integers that are factors of 8208. The greatest factor of 8208 is 8208.

3. What are the Factors of 8214?

Answer: Factors of 8214 are 1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214. There are 12 integers that are factors of 8214. The greatest factor of 8214 is 8214.

4. How to Find the GCF of 8208 and 8214?

Answer:

Greatest Common Factor of 8208 and 8214 = 6

Step 1: Find the prime factorization of 8208

8208 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 19

Step 2: Find the prime factorization of 8214

8214 = 2 x 3 x 37 x 37

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 8208 and 8214 is 6