Factors of 63
The factors of 63 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 63) or (-1, -63), 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 63, including all positive factors, factor pairs, and the prime factorization of 63 with step-by-step explanations and examples.
What are the Factors of 63?
There are 6 factors of 63. The factors of 63 are 1, 3, 7, 9, 21 and 63. Factors can be negative. The negative factors are -1, -3, -7, -9, -21 and -63. All of these numbers divides 63 completely. 63 is a composite number because it has other factors besides 1 and 63.
Factors of 63: 1, 3, 7, 9, 21 and 63
Factor Pairs of 63
The factor pairs of 63 are the pairs of integers that multiply together to give 63. These include both positive and negative combinations. The positive factor pairs of 63 are (1, 63), (3, 21), (7, 9), and the negative factor pairs are (-1, -63), (-3, -21), (-7, -9). Knowing the factor pairs of 63 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 63:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 63 |
| 3 | 21 |
| 7 | 9 |
Negative Factor Pairs of 63:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -63 |
| -3 | -21 |
| -7 | -9 |
Prime Factorization of 63
The prime factorization of 63 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 63 are 3, 3, 7. Therefore, the prime factorization of 63 is 3^2 × 7. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 63:
3, 3, 7
Prime factorization of 63:
3 × 3 × 7
Compact form:
32 × 7
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How to Find the Factors of 63?
To find the factors of 63 using the division method efficiently, you only need to check numbers up to the square root of 63. For every number that divides 63 evenly, both it and its corresponding pair (63 ÷ that number) are factors.
Optimized steps to find factors of 63:
- •63 ÷ 1 = 63 → ✅ Factor Pair: (1, 63)
- •63 ÷ 3 = 21 → ✅ Factor Pair: (3, 21)
- •63 ÷ 7 = 9 → ✅ Factor Pair: (7, 9)
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 63
What are the factors of 63?
The factors of 63 are 1, 3, 7, 9, 21, 63.
What is the prime factorization of 63?
The prime factorization of 63 is 3 × 3 × 7.
How do I find the factors of 63?
To find the factors of 63, start by dividing 63 by every number from 1 up to the square root of 63.
What are factor pairs of 63?
The factor pairs of 63 are (1, 63), (-1, -63), (3, 21), (-3, -21), (7, 9), (-7, -9).
How can I use the factors of 63?
The factors of 63 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 63 always positive?
Factors can be both positive and negative. For example, the negative factors of 63 are -1, -3, -7, -9, -21, -63.