The number 360
360 is a highly composite number: it has 24 divisors, more than any smaller number. Its prime factorisation is × × 5. Divisors (24): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36 … 360.
Pick any whole number from 1 to 100,000.
How to work it out
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What is special about 360: a highly composite number: it has 24 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.
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360 is composite. Its prime factorisation is
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The divisors add up to 1170; without 360 itself that is 810, so 360 is abundant (810 is more than 360). Euler's totient φ(360) = 96 numbers up to 360 share no factor with it.
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The digits of 360 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 19 steps to reach 1.
LaTeX source of the formulas on this page
\[ 360 = 2^{3} \times 3^{2} \times 5 \]360 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 1170 |
| Euler totient φ(n) | 96 |
| Square | 129600 |
| Cube | 46656000 |
| Square root | 18.973666 (= 6√10) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 19 |
| Scientific notation | 3.6 × |
360 in other forms
| Form | Value |
|---|---|
| In words | three hundred and sixty |
| Roman numerals | CCCLX |
| Binary (base 2) | 101101000 |
| Octal (base 8) | 550 |
| Hexadecimal (base 16) | 168 |
| Base 3 | 111100 |
| As time | 360 seconds = 6 min 0 s |
Is 360 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (360 ÷ 2 = 180) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (360 ÷ 3 = 120) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (360 ÷ 4 = 90) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (360 ÷ 5 = 72) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (360 ÷ 6 = 60) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (360 ÷ 8 = 45) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (360 ÷ 9 = 40) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (360 ÷ 10 = 36) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (360 ÷ 12 = 30) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 360 a prime number?
No. 360 = × × 5, so it is divisible by 2.
What are the 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.
What is 360 in binary?
101101000 (hexadecimal 168, octal 550).
What is the square root of 360?
About 18.9737, exactly 6√10.
What is 360 in Roman numerals?
CCCLX.
Is 360 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 360?
360 is a highly composite number: it has 24 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.