The number 31080
31080 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 7 × 37. Divisors (64): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28 … 31080.
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How to work it out
- 1
What is special about 31080: a Harshad number: divisible by its digit sum 12.
- 2
31080 is composite. Its prime factorisation is
- 3
The divisors add up to 109440; without 31080 itself that is 78360, so 31080 is abundant (78360 is more than 31080). Euler's totient φ(31080) = 6912 numbers up to 31080 share no factor with it.
- 4
The digits of 31080 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31080 = 2^{3} \times 3 \times 5 \times 7 \times 37 \]31080 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 109440 |
| Euler totient φ(n) | 6912 |
| Square | 965966400 |
| Cube | 30022235712000 |
| Square root | 176.295207 (= 2√7770) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 41 |
| Scientific notation | 3.108 × |
31080 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand and eighty |
| Binary (base 2) | 111100101101000 |
| Octal (base 8) | 74550 |
| Hexadecimal (base 16) | 7968 |
| Base 3 | 1120122010 |
| As time | 31080 seconds = 8 h 38 min 0 s |
Is 31080 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31080 ÷ 2 = 15540) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31080 ÷ 3 = 10360) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31080 ÷ 4 = 7770) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31080 ÷ 5 = 6216) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31080 ÷ 6 = 5180) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (31080 ÷ 7 = 4440) | 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 (31080 ÷ 8 = 3885) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (31080 ÷ 10 = 3108) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31080 ÷ 12 = 2590) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31080 a prime number?
No. 31080 = × 3 × 5 × 7 × 37, so it is divisible by 2.
What are the factors of 31080?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 37, 40, 42, 56, 60, 70, 74, 84, 105, 111, 120, 140, 148, 168, 185, 210, 222, 259, 280, 296, 370, 420, 444, 518, 555, 740, 777, 840, 888, 1036, 1110, 1295, 1480, 1554, 2072, 2220, 2590, 3108, 3885, 4440, 5180, 6216, 7770, 10360, 15540, 31080.
What is 31080 in binary?
111100101101000 (hexadecimal 7968, octal 74550).
What is the square root of 31080?
About 176.2952, exactly 2√7770.
Is 31080 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 31080?
31080 is a Harshad number: divisible by its digit sum 12.