Factors of 289
The factors of 289 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 289) or (-1, -289), and are always integers, never fractions or decimals. You can find them using methods such as division or prime factorization. Learning about factors helps build a foundation for understanding divisibility, multiples, and prime numbers. In this guide, we'll explore the different types of factors of 289, including all positive factors, factor pairs, and the prime factorization of 289 with step-by-step explanations and examples.
What are the Factors of 289?
There are 3 factors of 289. The factors of 289 are 1, 17 and 289. Factors can be negative. The negative factors are -1, -17 and -289. All of these numbers divides 289 completely. 289 is a composite number because it has other factors besides 1 and 289.
Factors of 289: 1, 17 and 289
Factor Pairs of 289
The factor pairs of 289 are the pairs of integers that multiply together to give 289. These include both positive and negative combinations. The positive factor pairs of 289 are (1, 289), (17, 17), and the negative factor pairs are (-1, -289), (-17, -17). Knowing the factor pairs of 289 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 289:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 289 |
| 17 | 17 |
Negative Factor Pairs of 289:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -289 |
| -17 | -17 |
Prime Factorization of 289
The prime factorization of 289 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 289 are 17, 17. Therefore, the prime factorization of 289 is 17^2. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 289:
17, 17
Prime factorization of 289:
17 × 17
Compact form:
172
Find prime factorization of any number with our Prime Factorization Calculator tool.
How to Find the Factors of 289?
To find the factors of 289 using the division method efficiently, you only need to check numbers up to the square root of 289. For every number that divides 289 evenly, both it and its corresponding pair (289 ÷ that number) are factors.
Optimized steps to find factors of 289:
- •289 ÷ 1 = 289 → ✅ Factor Pair: (1, 289)
- •289 ÷ 17 = 17 → ✅ Factor
This method avoids unnecessary checks and gives all factor pairs quickly. It's especially useful for larger numbers.
Find factors and factors pair of any number with our Factor Checker tool.
Frequently Asked Questions about factors of 289
What are the factors of 289?
The factors of 289 are 1, 17, 289.
What is the prime factorization of 289?
The prime factorization of 289 is 17 × 17.
How do I find the factors of 289?
To find the factors of 289, start by dividing 289 by every number from 1 up to the square root of 289.
What are factor pairs of 289?
The factor pairs of 289 are (1, 289), (-1, -289), (17, 17), (-17, -17).
How can I use the factors of 289?
The factors of 289 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 289 always positive?
Factors can be both positive and negative. For example, the negative factors of 289 are -1, -17, -289.