Greatest Common Factor of 289 and 296

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 289, 296 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 289 and 296 is 1.

GCF(289,296) = 1

GCF of 289 and 296

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

GCF of:
and

Greatest Common Factor of 289 and 296

GCF of 289 and 296 is 1

Prime Factorization of 289


17 289
17 17
1

Prime factors of 289 are 17. Prime factorization of 289 in exponential form is:

289 = 172

Prime Factorization of 296


2 296
2 148
2 74
37 37
1

Prime factors of 296 are 2.Prime factorization of 296 in exponential form is:

296 = 23×371

∴ So by taking common prime factors GCF of 289 and 296 is 1

Greatest Common Factor of 289 and 296 by matching factors method

Factors of 289

List of positive integer factors of 289 that divides 289 without a remainder.

1,17,289

Factors of 296

List of positive integer factors of 296 that divides 296 without a remainder.

1,2,4,8,37,74,148,296

Greatest Common Factor

We found the factors and prime factorization of 289 and 296. The biggest common factor number is the GCF number.
So the greatest common factor 289 and 296 is 1.

Also check out the Least Common Multiple of 289 and 296

Properties of GCF 289 and 296

(i) The GCF of 289 and 296 is associative

GCF of 289 and 296 = GCF of 296 and 289

Related Greatest Common Factor of 289

Related Greatest Common Factor of 296

Frequently Asked Questions on GCF of 289 and 296

1. What is the GCF of 289 and 296?

Answer: GCF of 289 and 296 is 1.

2. What are the Factors of 289?

Answer: Factors of 289 are 1, 17, 289. There are 3 integers that are factors of 289. The greatest factor of 289 is 289.

3. What are the Factors of 296?

Answer: Factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296. There are 8 integers that are factors of 296. The greatest factor of 296 is 296.

4. How to Find the GCF of 289 and 296?

Answer:

Greatest Common Factor of 289 and 296 = 1

Step 1: Find the prime factorization of 289

289 = 17 x 17

Step 2: Find the prime factorization of 296

296 = 2 x 2 x 2 x 37

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 289 and 296 is 1