Factors of 240
The factors of 240 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 240) or (-1, -240), 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 240, including all positive factors, factor pairs, and the prime factorization of 240 with step-by-step explanations and examples.
What are the Factors of 240?
There are 20 factors of 240. The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240. Factors can be negative. The negative factors are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -40, -48, -60, -80, -120 and -240. All of these numbers divides 240 completely. 240 is a composite number because it has other factors besides 1 and 240.
Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240
Factor Pairs of 240
The factor pairs of 240 are the pairs of integers that multiply together to give 240. These include both positive and negative combinations. The positive factor pairs of 240 are (1, 240), (2, 120), (3, 80), (4, 60), (5, 48), (6, 40), (8, 30), (10, 24), (12, 20), (15, 16), and the negative factor pairs are (-1, -240), (-2, -120), (-3, -80), (-4, -60), (-5, -48), (-6, -40), (-8, -30), (-10, -24), (-12, -20), (-15, -16). Knowing the factor pairs of 240 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 240:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 240 |
| 2 | 120 |
| 3 | 80 |
| 4 | 60 |
| 5 | 48 |
| 6 | 40 |
| 8 | 30 |
| 10 | 24 |
| 12 | 20 |
| 15 | 16 |
Negative Factor Pairs of 240:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -240 |
| -2 | -120 |
| -3 | -80 |
| -4 | -60 |
| -5 | -48 |
| -6 | -40 |
| -8 | -30 |
| -10 | -24 |
| -12 | -20 |
| -15 | -16 |
Prime Factorization of 240
The prime factorization of 240 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 240 are 2, 2, 2, 2, 3, 5. Therefore, the prime factorization of 240 is 2^4 × 3 × 5. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 240:
2, 2, 2, 2, 3, 5
Prime factorization of 240:
2 × 2 × 2 × 2 × 3 × 5
Compact form:
24 × 3 × 5
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How to Find the Factors of 240?
To find the factors of 240 using the division method efficiently, you only need to check numbers up to the square root of 240. For every number that divides 240 evenly, both it and its corresponding pair (240 ÷ that number) are factors.
Optimized steps to find factors of 240:
- •240 ÷ 1 = 240 → ✅ Factor Pair: (1, 240)
- •240 ÷ 2 = 120 → ✅ Factor Pair: (2, 120)
- •240 ÷ 3 = 80 → ✅ Factor Pair: (3, 80)
- •240 ÷ 4 = 60 → ✅ Factor Pair: (4, 60)
- •240 ÷ 5 = 48 → ✅ Factor Pair: (5, 48)
- •240 ÷ 6 = 40 → ✅ Factor Pair: (6, 40)
- •240 ÷ 8 = 30 → ✅ Factor Pair: (8, 30)
- •240 ÷ 10 = 24 → ✅ Factor Pair: (10, 24)
- •240 ÷ 12 = 20 → ✅ Factor Pair: (12, 20)
- •240 ÷ 15 = 16 → ✅ Factor Pair: (15, 16)
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 240
What are the factors of 240?
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.
What is the prime factorization of 240?
The prime factorization of 240 is 2 × 2 × 2 × 2 × 3 × 5.
How do I find the factors of 240?
To find the factors of 240, start by dividing 240 by every number from 1 up to the square root of 240.
What are factor pairs of 240?
The factor pairs of 240 are (1, 240), (-1, -240), (2, 120), (-2, -120), (3, 80), (-3, -80), (4, 60), (-4, -60), (5, 48), (-5, -48), (6, 40), (-6, -40), (8, 30), (-8, -30), (10, 24), (-10, -24), (12, 20), (-12, -20), (15, 16), (-15, -16).
How can I use the factors of 240?
The factors of 240 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 240 always positive?
Factors can be both positive and negative. For example, the negative factors of 240 are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -40, -48, -60, -80, -120, -240.