Factors of 360
The factors of 360 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 360) or (-1, -360), 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 360, including all positive factors, factor pairs, and the prime factorization of 360 with step-by-step explanations and examples.
What are the Factors of 360?
There are 24 factors of 360. The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360. Factors can be negative. The negative factors are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -30, -36, -40, -45, -60, -72, -90, -120, -180 and -360. All of these numbers divides 360 completely. 360 is a composite number because it has other factors besides 1 and 360.
Factors of 360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360
Factor Pairs of 360
The factor pairs of 360 are the pairs of integers that multiply together to give 360. These include both positive and negative combinations. The positive factor pairs of 360 are (1, 360), (2, 180), (3, 120), (4, 90), (5, 72), (6, 60), (8, 45), (9, 40), (10, 36), (12, 30), (15, 24), (18, 20), and the negative factor pairs are (-1, -360), (-2, -180), (-3, -120), (-4, -90), (-5, -72), (-6, -60), (-8, -45), (-9, -40), (-10, -36), (-12, -30), (-15, -24), (-18, -20). Knowing the factor pairs of 360 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 360:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 360 |
| 2 | 180 |
| 3 | 120 |
| 4 | 90 |
| 5 | 72 |
| 6 | 60 |
| 8 | 45 |
| 9 | 40 |
| 10 | 36 |
| 12 | 30 |
| 15 | 24 |
| 18 | 20 |
Negative Factor Pairs of 360:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -360 |
| -2 | -180 |
| -3 | -120 |
| -4 | -90 |
| -5 | -72 |
| -6 | -60 |
| -8 | -45 |
| -9 | -40 |
| -10 | -36 |
| -12 | -30 |
| -15 | -24 |
| -18 | -20 |
Prime Factorization of 360
The prime factorization of 360 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 360 are 2, 2, 2, 3, 3, 5. Therefore, the prime factorization of 360 is 2^3 × 3^2 × 5. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 360:
2, 2, 2, 3, 3, 5
Prime factorization of 360:
2 × 2 × 2 × 3 × 3 × 5
Compact form:
23 × 32 × 5
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How to Find the Factors of 360?
To find the factors of 360 using the division method efficiently, you only need to check numbers up to the square root of 360. For every number that divides 360 evenly, both it and its corresponding pair (360 ÷ that number) are factors.
Optimized steps to find factors of 360:
- •360 ÷ 1 = 360 → ✅ Factor Pair: (1, 360)
- •360 ÷ 2 = 180 → ✅ Factor Pair: (2, 180)
- •360 ÷ 3 = 120 → ✅ Factor Pair: (3, 120)
- •360 ÷ 4 = 90 → ✅ Factor Pair: (4, 90)
- •360 ÷ 5 = 72 → ✅ Factor Pair: (5, 72)
- •360 ÷ 6 = 60 → ✅ Factor Pair: (6, 60)
- •360 ÷ 8 = 45 → ✅ Factor Pair: (8, 45)
- •360 ÷ 9 = 40 → ✅ Factor Pair: (9, 40)
- •360 ÷ 10 = 36 → ✅ Factor Pair: (10, 36)
- •360 ÷ 12 = 30 → ✅ Factor Pair: (12, 30)
- •360 ÷ 15 = 24 → ✅ Factor Pair: (15, 24)
- •360 ÷ 18 = 20 → ✅ Factor Pair: (18, 20)
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 360
What are the factors of 360?
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.
What is the prime factorization of 360?
The prime factorization of 360 is 2 × 2 × 2 × 3 × 3 × 5.
How do I find the factors of 360?
To find the factors of 360, start by dividing 360 by every number from 1 up to the square root of 360.
What are factor pairs of 360?
The factor pairs of 360 are (1, 360), (-1, -360), (2, 180), (-2, -180), (3, 120), (-3, -120), (4, 90), (-4, -90), (5, 72), (-5, -72), (6, 60), (-6, -60), (8, 45), (-8, -45), (9, 40), (-9, -40), (10, 36), (-10, -36), (12, 30), (-12, -30), (15, 24), (-15, -24), (18, 20), (-18, -20).
How can I use the factors of 360?
The factors of 360 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 360 always positive?
Factors can be both positive and negative. For example, the negative factors of 360 are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -30, -36, -40, -45, -60, -72, -90, -120, -180, -360.