Factors of a number are integers that can be multiplied together to yield that number. For example, factors of 63 are numbers that, when multiplied in pairs, result in 63. The factors of 63 are 1, 3, 7, 9, 21, and 63. This article will explain how to determine these factors using different methods, including factorization and prime factorization.
What are the Factors of 63?
Factors of 63 are numbers that divide 63 exactly without leaving a remainder. These factors can be paired to give the product of 63. Since 63 is an odd composite number, it has several factors. The factors of 63 are:
1, 3, 7, 9, 21, 63
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Pair Factors of 63
Pair factors are pairs of numbers that, when multiplied together, result in the original number, 63. These pairs can be positive or negative.
Positive Pair Factors
- (1, 63)
- (3, 21)
- (7, 9)
Negative Pair Factors
- (-1, -63)
- (-3, -21)
- (-7, -9)
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Factors of 63 by Division Method
The division method involves dividing 63 by various integers to see which ones leave a remainder of 0. If there is no remainder, the divisor is a factor of 63. Here's how you can determine the factors of 63 using the division method:
| Division | Factor | Remainder |
|---|---|---|
| 63 ÷ 1 | 63 | 0 |
| 63 ÷ 3 | 21 | 0 |
| 63 ÷ 7 | 9 | 0 |
| 63 ÷ 9 | 7 | 0 |
| 63 ÷ 21 | 3 | 0 |
| 63 ÷ 63 | 1 | 0 |
If any number other than 1, 3, 7, 9, 21, or 63 is used to divide 63, it will leave a remainder.
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Prime Factorization of 63
Prime factorization is breaking down a number into its prime factors. For 63, the prime factors are 3 and 7.
Steps for prime factorization of 63:
- Divide 63 by 3 (the smallest prime number that can divide 63 without leaving a fraction).
- 63 ÷ 3 = 21
- Divide 21 by 3 again.
- 21 ÷ 3 = 7
- Finally, divide 7 by 7 (since 7 is also a prime number).
- 7 ÷ 7 = 1
Thus, the prime factorization of 63 is 3×3×7 or 32×7
Also Check: Cube root table
Examples
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Rectangle Area Example:
- A rectangle has a surface area of 63 square inches and a length of 21 inches. What is the width?
- Area = length × width → 63 = 21 × width → width = 63 ÷ 21 = 3 inches.
-
Product of Prime Factors:
- What is the product of the prime factors of 63?
- Prime factors are 3 and 7.
- Product = 3×7=213 \times 7 = 213×7=21.
-
Common Factors of 63 and 62:
- Factors of 63: 1, 3, 7, 9, 21, 63.
- Factors of 62: 1, 2, 31, 62.
- Common factor: 1.
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Common Factors of 63 and 64:
- Factors of 63: 1, 3, 7, 9, 21, 63.
- Factors of 64: 1, 2, 4, 8, 16, 32, 64.
- Common factor: 1.
-
Common Factors of 63 and 61:
- Factors of 63: 1, 3, 7, 9, 21, 63.
- Factors of 61: 1, 61.
- Common factor: 1.
Understanding the factors of 63 helps in various mathematical applications, including solving problems related to division, prime factorization, and finding common factors between numbers. This comprehensive guide provides clarity on calculating and utilizing the factors of 63.
Frequently Asked Questions
The factors of 63 are the numbers that divide 63 without leaving a remainder. They are 1, 3, 7, 9, 21, and 63.
The prime factorization of 63 is 3 × 3 × 7, or expressed as exponents, 3² × 7.
The positive pair factors of 63 are (1, 63), (3, 21), and (7, 9).
The negative pair factors of 63 are (-1, -63), (-3, -21), and (-7, -9).
Yes, 21 is a factor of 63 because it divides 63 exactly without leaving a remainder.