Factors of 168
The factors of 168 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 168) or (-1, -168), 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 168, including all positive factors, factor pairs, and the prime factorization of 168 with step-by-step explanations and examples.
What are the Factors of 168?
There are 16 factors of 168. The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84 and 168. Factors can be negative. The negative factors are -1, -2, -3, -4, -6, -7, -8, -12, -14, -21, -24, -28, -42, -56, -84 and -168. All of these numbers divides 168 completely. 168 is a composite number because it has other factors besides 1 and 168.
Factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84 and 168
Factor Pairs of 168
The factor pairs of 168 are the pairs of integers that multiply together to give 168. These include both positive and negative combinations. The positive factor pairs of 168 are (1, 168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21), (12, 14), and the negative factor pairs are (-1, -168), (-2, -84), (-3, -56), (-4, -42), (-6, -28), (-7, -24), (-8, -21), (-12, -14). Knowing the factor pairs of 168 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 168:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 168 |
| 2 | 84 |
| 3 | 56 |
| 4 | 42 |
| 6 | 28 |
| 7 | 24 |
| 8 | 21 |
| 12 | 14 |
Negative Factor Pairs of 168:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -168 |
| -2 | -84 |
| -3 | -56 |
| -4 | -42 |
| -6 | -28 |
| -7 | -24 |
| -8 | -21 |
| -12 | -14 |
Prime Factorization of 168
The prime factorization of 168 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 168 are 2, 2, 2, 3, 7. Therefore, the prime factorization of 168 is 2^3 × 3 × 7. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 168:
2, 2, 2, 3, 7
Prime factorization of 168:
2 × 2 × 2 × 3 × 7
Compact form:
23 × 3 × 7
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How to Find the Factors of 168?
To find the factors of 168 using the division method efficiently, you only need to check numbers up to the square root of 168. For every number that divides 168 evenly, both it and its corresponding pair (168 ÷ that number) are factors.
Optimized steps to find factors of 168:
- •168 ÷ 1 = 168 → ✅ Factor Pair: (1, 168)
- •168 ÷ 2 = 84 → ✅ Factor Pair: (2, 84)
- •168 ÷ 3 = 56 → ✅ Factor Pair: (3, 56)
- •168 ÷ 4 = 42 → ✅ Factor Pair: (4, 42)
- •168 ÷ 6 = 28 → ✅ Factor Pair: (6, 28)
- •168 ÷ 7 = 24 → ✅ Factor Pair: (7, 24)
- •168 ÷ 8 = 21 → ✅ Factor Pair: (8, 21)
- •168 ÷ 12 = 14 → ✅ Factor Pair: (12, 14)
This method avoids unnecessary checks and gives all factor pairs quickly. It's especially useful for larger numbers.
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Frequently Asked Questions about factors of 168
What are the factors of 168?
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
What is the prime factorization of 168?
The prime factorization of 168 is 2 × 2 × 2 × 3 × 7.
How do I find the factors of 168?
To find the factors of 168, start by dividing 168 by every number from 1 up to the square root of 168.
What are factor pairs of 168?
The factor pairs of 168 are (1, 168), (-1, -168), (2, 84), (-2, -84), (3, 56), (-3, -56), (4, 42), (-4, -42), (6, 28), (-6, -28), (7, 24), (-7, -24), (8, 21), (-8, -21), (12, 14), (-12, -14).
How can I use the factors of 168?
The factors of 168 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 168 always positive?
Factors can be both positive and negative. For example, the negative factors of 168 are -1, -2, -3, -4, -6, -7, -8, -12, -14, -21, -24, -28, -42, -56, -84, -168.