Factors of 135
The factors of 135 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 135) or (-1, -135), 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 135, including all positive factors, factor pairs, and the prime factorization of 135 with step-by-step explanations and examples.
What are the Factors of 135?
There are 8 factors of 135. The factors of 135 are 1, 3, 5, 9, 15, 27, 45 and 135. Factors can be negative. The negative factors are -1, -3, -5, -9, -15, -27, -45 and -135. All of these numbers divides 135 completely. 135 is a composite number because it has other factors besides 1 and 135.
Factors of 135: 1, 3, 5, 9, 15, 27, 45 and 135
Factor Pairs of 135
The factor pairs of 135 are the pairs of integers that multiply together to give 135. These include both positive and negative combinations. The positive factor pairs of 135 are (1, 135), (3, 45), (5, 27), (9, 15), and the negative factor pairs are (-1, -135), (-3, -45), (-5, -27), (-9, -15). Knowing the factor pairs of 135 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 135:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 135 |
| 3 | 45 |
| 5 | 27 |
| 9 | 15 |
Negative Factor Pairs of 135:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -135 |
| -3 | -45 |
| -5 | -27 |
| -9 | -15 |
Prime Factorization of 135
The prime factorization of 135 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 135 are 3, 3, 3, 5. Therefore, the prime factorization of 135 is 3^3 × 5. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 135:
3, 3, 3, 5
Prime factorization of 135:
3 × 3 × 3 × 5
Compact form:
33 × 5
Find prime factorization of any number with our Prime Factorization Calculator tool.
How to Find the Factors of 135?
To find the factors of 135 using the division method efficiently, you only need to check numbers up to the square root of 135. For every number that divides 135 evenly, both it and its corresponding pair (135 ÷ that number) are factors.
Optimized steps to find factors of 135:
- •135 ÷ 1 = 135 → ✅ Factor Pair: (1, 135)
- •135 ÷ 3 = 45 → ✅ Factor Pair: (3, 45)
- •135 ÷ 5 = 27 → ✅ Factor Pair: (5, 27)
- •135 ÷ 9 = 15 → ✅ Factor Pair: (9, 15)
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 135
What are the factors of 135?
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135.
What is the prime factorization of 135?
The prime factorization of 135 is 3 × 3 × 3 × 5.
How do I find the factors of 135?
To find the factors of 135, start by dividing 135 by every number from 1 up to the square root of 135.
What are factor pairs of 135?
The factor pairs of 135 are (1, 135), (-1, -135), (3, 45), (-3, -45), (5, 27), (-5, -27), (9, 15), (-9, -15).
How can I use the factors of 135?
The factors of 135 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 135 always positive?
Factors can be both positive and negative. For example, the negative factors of 135 are -1, -3, -5, -9, -15, -27, -45, -135.