Greatest Common Factor of 17208 and 17214

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 17208, 17214 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 17208 and 17214 is 6.

GCF(17208,17214) = 6

GCF of 17208 and 17214

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

GCF of:
and

Greatest Common Factor of 17208 and 17214

GCF of 17208 and 17214 is 6

Prime Factorization of 17208


2 17208
2 8604
2 4302
3 2151
3 717
239 239
1

Prime factors of 17208 are 2,3,239. Prime factorization of 17208 in exponential form is:

17208 = 23×32×2391

Prime Factorization of 17214


2 17214
3 8607
19 2869
151 151
1

Prime factors of 17214 are 2,3,19,151. Prime factorization of 17214 in exponential form is:

17214 = 21×31×191×1511

∴ So by taking common prime factors GCF of 17208 and 17214 is 6

Greatest Common Factor of 17208 and 17214 by matching factors method

Factors of 17208

List of positive integer factors of 17208 that divides 17208 without a remainder.

1,2,3,4,6,8,9,12,18,24,36,72,239,478,717,956,1434,1912,2151,2868,4302,5736,8604,17208

Factors of 17214

List of positive integer factors of 17214 that divides 17214 without a remainder.

1,2,3,6,19,38,57,114,151,302,453,906,2869,5738,8607,17214

Greatest Common Factor

We found the factors and prime factorization of 17208 and 17214. The biggest common factor number is the GCF number.
So the greatest common factor 17208 and 17214 is 6.

Also check out the Least Common Multiple of 17208 and 17214

Properties of GCF 17208 and 17214

(i) The GCF of 17208 and 17214 is associative

GCF of 17208 and 17214 = GCF of 17214 and 17208

Related Greatest Common Factor of 17208

Related Greatest Common Factor of 17214

Frequently Asked Questions on GCF of 17208 and 17214

1. What is the GCF of 17208 and 17214?

Answer: GCF of 17208 and 17214 is 6.

2. What are the Factors of 17208?

Answer: Factors of 17208 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 239, 478, 717, 956, 1434, 1912, 2151, 2868, 4302, 5736, 8604, 17208. There are 24 integers that are factors of 17208. The greatest factor of 17208 is 17208.

3. What are the Factors of 17214?

Answer: Factors of 17214 are 1, 2, 3, 6, 19, 38, 57, 114, 151, 302, 453, 906, 2869, 5738, 8607, 17214. There are 16 integers that are factors of 17214. The greatest factor of 17214 is 17214.

4. How to Find the GCF of 17208 and 17214?

Answer:

Greatest Common Factor of 17208 and 17214 = 6

Step 1: Find the prime factorization of 17208

17208 = 2 x 2 x 2 x 3 x 3 x 239

Step 2: Find the prime factorization of 17214

17214 = 2 x 3 x 19 x 151

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 17208 and 17214 is 6