Greatest Common Factor of 288 and 289

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 288, 289 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 288 and 289 is 1.

GCF(288,289) = 1

GCF of 288 and 289

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

GCF of:
and

Greatest Common Factor of 288 and 289

GCF of 288 and 289 is 1

Prime Factorization of 288


2 288
2 144
2 72
2 36
2 18
3 9
3 3
1

Prime factors of 288 are 2,3. Prime factorization of 288 in exponential form is:

288 = 25×32

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

∴ So by taking common prime factors GCF of 288 and 289 is 1

Greatest Common Factor of 288 and 289 by matching factors method

Factors of 288

List of positive integer factors of 288 that divides 288 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288

Factors of 289

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

1,17,289

Greatest Common Factor

We found the factors and prime factorization of 288 and 289. The biggest common factor number is the GCF number.
So the greatest common factor 288 and 289 is 1.

Also check out the Least Common Multiple of 288 and 289

Properties of GCF 288 and 289

(i) The GCF of 288 and 289 is associative

GCF of 288 and 289 = GCF of 289 and 288

Related Greatest Common Factor of 288

Related Greatest Common Factor of 289

Frequently Asked Questions on GCF of 288 and 289

1. What is the GCF of 288 and 289?

Answer: GCF of 288 and 289 is 1.

2. What are the Factors of 288?

Answer: Factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288. There are 18 integers that are factors of 288. The greatest factor of 288 is 288.

3. 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.

4. How to Find the GCF of 288 and 289?

Answer:

Greatest Common Factor of 288 and 289 = 1

Step 1: Find the prime factorization of 288

288 = 2 x 2 x 2 x 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 289

289 = 17 x 17

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 288 and 289 is 1