Factors of 800
The factors of 800 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 800) or (-1, -800), 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 800, including all positive factors, factor pairs, and the prime factorization of 800 with step-by-step explanations and examples.
What are the Factors of 800?
There are 18 factors of 800. The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400 and 800. Factors can be negative. The negative factors are -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -80, -100, -160, -200, -400 and -800. All of these numbers divides 800 completely. 800 is a composite number because it has other factors besides 1 and 800.
Factors of 800: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400 and 800
Factor Pairs of 800
The factor pairs of 800 are the pairs of integers that multiply together to give 800. These include both positive and negative combinations. The positive factor pairs of 800 are (1, 800), (2, 400), (4, 200), (5, 160), (8, 100), (10, 80), (16, 50), (20, 40), (25, 32), and the negative factor pairs are (-1, -800), (-2, -400), (-4, -200), (-5, -160), (-8, -100), (-10, -80), (-16, -50), (-20, -40), (-25, -32). Knowing the factor pairs of 800 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 800:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 800 |
| 2 | 400 |
| 4 | 200 |
| 5 | 160 |
| 8 | 100 |
| 10 | 80 |
| 16 | 50 |
| 20 | 40 |
| 25 | 32 |
Negative Factor Pairs of 800:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -800 |
| -2 | -400 |
| -4 | -200 |
| -5 | -160 |
| -8 | -100 |
| -10 | -80 |
| -16 | -50 |
| -20 | -40 |
| -25 | -32 |
Prime Factorization of 800
The prime factorization of 800 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 800 are 2, 2, 2, 2, 2, 5, 5. Therefore, the prime factorization of 800 is 2^5 × 5^2. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 800:
2, 2, 2, 2, 2, 5, 5
Prime factorization of 800:
2 × 2 × 2 × 2 × 2 × 5 × 5
Compact form:
25 × 52
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How to Find the Factors of 800?
To find the factors of 800 using the division method efficiently, you only need to check numbers up to the square root of 800. For every number that divides 800 evenly, both it and its corresponding pair (800 ÷ that number) are factors.
Optimized steps to find factors of 800:
- •800 ÷ 1 = 800 → ✅ Factor Pair: (1, 800)
- •800 ÷ 2 = 400 → ✅ Factor Pair: (2, 400)
- •800 ÷ 4 = 200 → ✅ Factor Pair: (4, 200)
- •800 ÷ 5 = 160 → ✅ Factor Pair: (5, 160)
- •800 ÷ 8 = 100 → ✅ Factor Pair: (8, 100)
- •800 ÷ 10 = 80 → ✅ Factor Pair: (10, 80)
- •800 ÷ 16 = 50 → ✅ Factor Pair: (16, 50)
- •800 ÷ 20 = 40 → ✅ Factor Pair: (20, 40)
- •800 ÷ 25 = 32 → ✅ Factor Pair: (25, 32)
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 800
What are the factors of 800?
The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800.
What is the prime factorization of 800?
The prime factorization of 800 is 2 × 2 × 2 × 2 × 2 × 5 × 5.
How do I find the factors of 800?
To find the factors of 800, start by dividing 800 by every number from 1 up to the square root of 800.
What are factor pairs of 800?
The factor pairs of 800 are (1, 800), (-1, -800), (2, 400), (-2, -400), (4, 200), (-4, -200), (5, 160), (-5, -160), (8, 100), (-8, -100), (10, 80), (-10, -80), (16, 50), (-16, -50), (20, 40), (-20, -40), (25, 32), (-25, -32).
How can I use the factors of 800?
The factors of 800 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 800 always positive?
Factors can be both positive and negative. For example, the negative factors of 800 are -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -80, -100, -160, -200, -400, -800.