The number 31488
31488 is a composite number with 36 divisors. Its prime factorisation is × 3 × 41. Divisors (36): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 41, 48, 64, 82, 96, 123 … 31488.
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How to work it out
- 1
What is special about 31488: a Harshad number: divisible by its digit sum 24.
- 2
31488 is composite. Its prime factorisation is
- 3
The divisors add up to 85848; without 31488 itself that is 54360, so 31488 is abundant (54360 is more than 31488). Euler's totient φ(31488) = 10240 numbers up to 31488 share no factor with it.
- 4
The digits of 31488 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31488 = 2^{8} \times 3 \times 41 \]31488 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 85848 |
| Euler totient φ(n) | 10240 |
| Square | 991494144 |
| Cube | 31220167606272 |
| Square root | 177.448584 (= 16√123) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.1488 × |
31488 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand four hundred and eighty-eight |
| Binary (base 2) | 111101100000000 |
| Octal (base 8) | 75400 |
| Hexadecimal (base 16) | 7B00 |
| Base 3 | 1121012020 |
| As time | 31488 seconds = 8 h 44 min 48 s |
Is 31488 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31488 ÷ 2 = 15744) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31488 ÷ 3 = 10496) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31488 ÷ 4 = 7872) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31488 ÷ 6 = 5248) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (31488 ÷ 8 = 3936) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31488 ÷ 12 = 2624) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31488 a prime number?
No. 31488 = × 3 × 41, so it is divisible by 2.
What are the factors of 31488?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 41, 48, 64, 82, 96, 123, 128, 164, 192, 246, 256, 328, 384, 492, 656, 768, 984, 1312, 1968, 2624, 3936, 5248, 7872, 10496, 15744, 31488.
What is 31488 in binary?
111101100000000 (hexadecimal 7B00, octal 75400).
What is the square root of 31488?
About 177.4486, exactly 16√123.
Is 31488 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 31488?
31488 is a Harshad number: divisible by its digit sum 24.