Factors of 675
The factors of 675 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 675) or (-1, -675), 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 675, including all positive factors, factor pairs, and the prime factorization of 675 with step-by-step explanations and examples.
What are the Factors of 675?
There are 12 factors of 675. The factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225 and 675. Factors can be negative. The negative factors are -1, -3, -5, -9, -15, -25, -27, -45, -75, -135, -225 and -675. All of these numbers divides 675 completely. 675 is a composite number because it has other factors besides 1 and 675.
Factors of 675: 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225 and 675
Factor Pairs of 675
The factor pairs of 675 are the pairs of integers that multiply together to give 675. These include both positive and negative combinations. The positive factor pairs of 675 are (1, 675), (3, 225), (5, 135), (9, 75), (15, 45), (25, 27), and the negative factor pairs are (-1, -675), (-3, -225), (-5, -135), (-9, -75), (-15, -45), (-25, -27). Knowing the factor pairs of 675 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 675:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 675 |
| 3 | 225 |
| 5 | 135 |
| 9 | 75 |
| 15 | 45 |
| 25 | 27 |
Negative Factor Pairs of 675:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -675 |
| -3 | -225 |
| -5 | -135 |
| -9 | -75 |
| -15 | -45 |
| -25 | -27 |
Prime Factorization of 675
The prime factorization of 675 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 675 are 3, 3, 3, 5, 5. Therefore, the prime factorization of 675 is 3^3 × 5^2. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 675:
3, 3, 3, 5, 5
Prime factorization of 675:
3 × 3 × 3 × 5 × 5
Compact form:
33 × 52
Find prime factorization of any number with our Prime Factorization Calculator tool.
How to Find the Factors of 675?
To find the factors of 675 using the division method efficiently, you only need to check numbers up to the square root of 675. For every number that divides 675 evenly, both it and its corresponding pair (675 ÷ that number) are factors.
Optimized steps to find factors of 675:
- •675 ÷ 1 = 675 → ✅ Factor Pair: (1, 675)
- •675 ÷ 3 = 225 → ✅ Factor Pair: (3, 225)
- •675 ÷ 5 = 135 → ✅ Factor Pair: (5, 135)
- •675 ÷ 9 = 75 → ✅ Factor Pair: (9, 75)
- •675 ÷ 15 = 45 → ✅ Factor Pair: (15, 45)
- •675 ÷ 25 = 27 → ✅ Factor Pair: (25, 27)
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 675
What are the factors of 675?
The factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675.
What is the prime factorization of 675?
The prime factorization of 675 is 3 × 3 × 3 × 5 × 5.
How do I find the factors of 675?
To find the factors of 675, start by dividing 675 by every number from 1 up to the square root of 675.
What are factor pairs of 675?
The factor pairs of 675 are (1, 675), (-1, -675), (3, 225), (-3, -225), (5, 135), (-5, -135), (9, 75), (-9, -75), (15, 45), (-15, -45), (25, 27), (-25, -27).
How can I use the factors of 675?
The factors of 675 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 675 always positive?
Factors can be both positive and negative. For example, the negative factors of 675 are -1, -3, -5, -9, -15, -25, -27, -45, -75, -135, -225, -675.