Introduction
Numbers are a fundamental part of our everyday lives, and understanding them helps us solve various problems. One key concept in mathematics is the study of factors. Factors are numbers that divide a given integer without leaving a remainder. In this guide, we'll explore the factors of 8, learn different methods to find these factors, and answer some common questions.
What are the Factors of 8?
The factors of 8 are the numbers that can divide 8 without leaving a remainder. In simpler terms, the numbers that multiply together to make 8 are its factors. These factors include 1, 2, 4, and 8.
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Positive and Negative Pair Factors of 8
Factors can be both positive and negative. For every positive factor pair, there is a corresponding negative pair.
Positive Pair Factors of 8
| Factor Pair | Product |
|---|---|
| (1, 8) | 1 x 8 = 8 |
| (2, 4) | 2 x 4 = 8 |
Negative Pair Factors of 8
| Factor Pair | Product |
|---|---|
| (-1, -8) | -1 x -8 = 8 |
| (-2, -4) | -2 x -4 = 8 |
Methods to Find the Factors of 8
Prime Factorization Method
Prime factorization involves breaking down a number into its prime factors. For 8, the prime factorization is:
8=2×2×2=23
So, the prime factors of 8 are 2, and the factors are 1, 2, 4, and 8.
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Listing Method
The listing method involves listing all positive integers that divide 8 evenly. We list numbers from 1 to 8 and see which ones divide 8 without a remainder.
| Number | Division Result | Factor? |
|---|---|---|
| 1 | 8 ÷ 1 = 8 | Yes |
| 2 | 8 ÷ 2 = 4 | Yes |
| 3 | 8 ÷ 3 = 2.67 | No |
| 4 | 8 ÷ 4 = 2 | Yes |
| 5 | 8 ÷ 5 = 1.6 | No |
| 6 | 8 ÷ 6 = 1.33 | No |
| 7 | 8 ÷ 7 = 1.14 | No |
| 8 | 8 ÷ 8 = 1 | Yes |
Division Method
The division method involves dividing 8 by all numbers less than or equal to it. If the result is a whole number, the divisor is a factor of 8.
- 8÷1=88 ÷ 1 = 88÷1=8 (Factors: 1 and 8)
- 8÷2=48 ÷ 2 = 48÷2=4 (Factors: 2 and 4)
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Solved Examples
Example 1: Find the positive factors of 8.
Answer: The positive factors of 8 are 1, 2, 4, and 8.
Example 2: Find the negative factors of 8.
Answer: The negative factors of 8 are -1, -2, -4, and -8.
Example 3: Find the prime factorization of 36.
Answer: The prime factorization of 36 is 2×2×3×3=22×32
Frequently Asked Questions
No, 8 has more than 2 factors. The factors of 8 are the integers that can be evenly divided into 8. These factors are 1, 2, 4, and 8, with 8 being the largest.
No, 16 is not a factor of 8. However, 8 is a factor of 16. The factors of 8 are 1, 2, 4, and 8, while the factors of 16 include 1, 2, 4, 8, and 16.
The factors of 8 are the numbers that divide 8 exactly without leaving a remainder. The factors of 8 are 1, 2, 4, and 8.
2 is a factor of 8 because when you divide 8 by 2, the quotient is 4 and the remainder is 0. Since 4 is also a factor of 8, this confirms that 2 is a factor of 8.