Factors of 360
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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, 360
Summary
360 has 24 factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 (sum of all factors: 1,170).
Total Factors
24
Is Prime?
No
Perfect Square?
No
All factors, smallest to largest
What is a Factor Calculator?
A factor (or divisor) of a whole number is any whole number that divides it evenly, leaving no remainder. This calculator lists every positive factor of a number you enter, pairs them up (since factors always come in pairs that multiply back to the original number), and tells you whether the number is prime or a perfect square.
Every number has at least two factors — 1 and itself — except prime numbers, which have exactly those two and nothing else. Numbers with many factors (called "highly composite" numbers, like 12, 24, and 360) are especially useful in everyday math because they divide evenly by so many smaller numbers.
Factor Pairs of 360
Each pair multiplies together to produce 360.
| Factor A | Factor B | Product |
|---|---|---|
| 1 | 360 | 360 |
| 2 | 180 | 360 |
| 3 | 120 | 360 |
| 4 | 90 | 360 |
| 5 | 72 | 360 |
| 6 | 60 | 360 |
| 8 | 45 | 360 |
| 9 | 40 | 360 |
| 10 | 36 | 360 |
| 12 | 30 | 360 |
| 15 | 24 | 360 |
| 18 | 20 | 360 |
How to Find All Factors of a Number
The fastest method checks only whole numbers up to the square root of the target number. For each one that divides evenly, both it and its "partner" (the number divided by it) are factors — so you only need to test roughly √n candidates to find all of n's factors, not all n of them.
Perfect Squares Have an Odd Number of Factors
Most numbers have an even number of factors, since they pair up neatly (1 with n, 2 with n/2, and so on). Perfect squares are the exception: their square root pairs with itself, so it only counts once, leaving an odd total. For example, 36 = 6² has 9 factors (1, 2, 3, 4, 6, 9, 12, 18, 36) — an odd count, because 6 pairs with itself.
Factor Calculator vs. Prime Factorization
This calculator lists every divisor of a number — prime and composite alike. The Prime Factorization Calculator instead breaks the number down into only its prime building blocks. The two are connected: every factor listed here can be formed by multiplying some combination of the number's prime factors together.
Practical Uses for Factors
Factoring shows up constantly in everyday math: simplifying fractions relies on finding common factors between numerator and denominator, splitting a group evenly (into teams, rows, or portions) relies on finding factors of the group size, and factoring polynomials in algebra directly extends the same idea from whole numbers to expressions.
Example — Your Current Input
360 has 24 factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 (sum of all factors: 1,170).
Additional Example — Factors of 100
Checking whole numbers up to √100 = 10: 1 pairs with 100, 2 with 50, 4 with 25, 5 with 20, and 10 pairs with itself (since 10 × 10 = 100). That gives the complete list — 1, 2, 4, 5, 10, 20, 25, 50, 100 — nine factors total, an odd number, which makes sense since 100 is a perfect square (10²).
About This Parameter
- Number
- Any whole number of 1 or greater. The number 1 has exactly one factor (itself); every other number has at least two (1 and itself).
Frequently Asked Questions
What's the difference between a factor and a multiple?
A factor of n divides n evenly (factors of 12 include 1, 2, 3, 4, 6, 12 — all ≤ 12). A multiple of n is what you get multiplying n by a whole number (multiples of 12 are 12, 24, 36, 48, … — all ≥ 12, extending infinitely). They're opposite directions of the same relationship.
Are negative numbers factors too?
Mathematically, negative numbers can also divide evenly (−2 divides 12 just as 2 does), so technically every positive factor has a negative counterpart. This calculator lists only positive factors, which is the standard convention for most practical uses.
How is this different from the Greatest Common Factor Calculator?
The GCF Calculator finds the largest factor shared between two or more numbers. This Factor Calculator instead lists every factor of a single number on its own — a different (though related) question.
What is a "perfect number"?
A perfect number equals the sum of its factors excluding itself — 6 is the smallest example, since 1 + 2 + 3 = 6. This calculator's "sum of all factors" figure includes the number itself, so a perfect number's sum will equal exactly double the number.