Factors of 361
The factors of 361 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 361) or (-1, -361), 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 361, including all positive factors, factor pairs, and the prime factorization of 361 with step-by-step explanations and examples.
What are the Factors of 361?
There are 3 factors of 361. The factors of 361 are 1, 19 and 361. Factors can be negative. The negative factors are -1, -19 and -361. All of these numbers divides 361 completely. 361 is a composite number because it has other factors besides 1 and 361.
Factors of 361: 1, 19 and 361
Factor Pairs of 361
The factor pairs of 361 are the pairs of integers that multiply together to give 361. These include both positive and negative combinations. The positive factor pairs of 361 are (1, 361), (19, 19), and the negative factor pairs are (-1, -361), (-19, -19). Knowing the factor pairs of 361 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 361:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 361 |
| 19 | 19 |
Negative Factor Pairs of 361:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -361 |
| -19 | -19 |
Prime Factorization of 361
The prime factorization of 361 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 361 are 19, 19. Therefore, the prime factorization of 361 is 19^2. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 361:
19, 19
Prime factorization of 361:
19 × 19
Compact form:
192
Find prime factorization of any number with our Prime Factorization Calculator tool.
How to Find the Factors of 361?
To find the factors of 361 using the division method efficiently, you only need to check numbers up to the square root of 361. For every number that divides 361 evenly, both it and its corresponding pair (361 ÷ that number) are factors.
Optimized steps to find factors of 361:
- •361 ÷ 1 = 361 → ✅ Factor Pair: (1, 361)
- •361 ÷ 19 = 19 → ✅ 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 361
What are the factors of 361?
The factors of 361 are 1, 19, 361.
What is the prime factorization of 361?
The prime factorization of 361 is 19 × 19.
How do I find the factors of 361?
To find the factors of 361, start by dividing 361 by every number from 1 up to the square root of 361.
What are factor pairs of 361?
The factor pairs of 361 are (1, 361), (-1, -361), (19, 19), (-19, -19).
How can I use the factors of 361?
The factors of 361 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 361 always positive?
Factors can be both positive and negative. For example, the negative factors of 361 are -1, -19, -361.