The number 31140
31140 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 173. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60 … 31140.
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How to work it out
- 1
What is special about 31140: a Harshad number: divisible by its digit sum 9.
- 2
31140 is composite. Its prime factorisation is
- 3
The divisors add up to 95004; without 31140 itself that is 63864, so 31140 is abundant (63864 is more than 31140). Euler's totient φ(31140) = 8256 numbers up to 31140 share no factor with it.
- 4
The digits of 31140 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 222 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31140 = 2^{2} \times 3^{2} \times 5 \times 173 \]31140 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 95004 |
| Euler totient φ(n) | 8256 |
| Square | 969699600 |
| Cube | 30196445544000 |
| Square root | 176.465294 (= 6√865) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 222 |
| Scientific notation | 3.114 × |
31140 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand one hundred and forty |
| Binary (base 2) | 111100110100100 |
| Octal (base 8) | 74644 |
| Hexadecimal (base 16) | 79A4 |
| Base 3 | 1120201100 |
| As time | 31140 seconds = 8 h 39 min 0 s |
Is 31140 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31140 ÷ 2 = 15570) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31140 ÷ 3 = 10380) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31140 ÷ 4 = 7785) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31140 ÷ 5 = 6228) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31140 ÷ 6 = 5190) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (31140 ÷ 9 = 3460) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (31140 ÷ 10 = 3114) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31140 ÷ 12 = 2595) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31140 a prime number?
No. 31140 = × × 5 × 173, so it is divisible by 2.
What are the factors of 31140?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 173, 180, 346, 519, 692, 865, 1038, 1557, 1730, 2076, 2595, 3114, 3460, 5190, 6228, 7785, 10380, 15570, 31140.
What is 31140 in binary?
111100110100100 (hexadecimal 79A4, octal 74644).
What is the square root of 31140?
About 176.4653, exactly 6√865.
Is 31140 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 31140?
31140 is a Harshad number: divisible by its digit sum 9.