Greatest Common Factor of 17214 and 17216

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 17214, 17216 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 17214 and 17216 is 2.

GCF(17214,17216) = 2

GCF of 17214 and 17216

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

GCF of:
and

Greatest Common Factor of 17214 and 17216

GCF of 17214 and 17216 is 2

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

Prime Factorization of 17216


2 17216
2 8608
2 4304
2 2152
2 1076
2 538
269 269
1

Prime factors of 17216 are 2,269. Prime factorization of 17216 in exponential form is:

17216 = 26×2691

∴ So by taking common prime factors GCF of 17214 and 17216 is 2

Greatest Common Factor of 17214 and 17216 by matching factors method

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

Factors of 17216

List of positive integer factors of 17216 that divides 17216 without a remainder.

1,2,4,8,16,32,64,269,538,1076,2152,4304,8608,17216

Greatest Common Factor

We found the factors and prime factorization of 17214 and 17216. The biggest common factor number is the GCF number.
So the greatest common factor 17214 and 17216 is 2.

Also check out the Least Common Multiple of 17214 and 17216

Properties of GCF 17214 and 17216

(i) The GCF of 17214 and 17216 is associative

GCF of 17214 and 17216 = GCF of 17216 and 17214

Related Greatest Common Factor of 17214

Related Greatest Common Factor of 17216

Frequently Asked Questions on GCF of 17214 and 17216

1. What is the GCF of 17214 and 17216?

Answer: GCF of 17214 and 17216 is 2.

2. 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.

3. What are the Factors of 17216?

Answer: Factors of 17216 are 1, 2, 4, 8, 16, 32, 64, 269, 538, 1076, 2152, 4304, 8608, 17216. There are 14 integers that are factors of 17216. The greatest factor of 17216 is 17216.

4. How to Find the GCF of 17214 and 17216?

Answer:

Greatest Common Factor of 17214 and 17216 = 2

Step 1: Find the prime factorization of 17214

17214 = 2 x 3 x 19 x 151

Step 2: Find the prime factorization of 17216

17216 = 2 x 2 x 2 x 2 x 2 x 2 x 269

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

GCF = 2

Step 4: Therefore, the greatest common factor of 17214 and 17216 is 2