The number 47988
47988 is a composite number with 36 divisors. Its prime factorisation is × × 31 × 43. Divisors (36): 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 43, 62, 86, 93, 124, 129 … 47988.
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How to work it out
- 1
What is special about 47988: a Harshad number: divisible by its digit sum 36.
- 2
47988 is composite. Its prime factorisation is
- 3
The divisors add up to 128128; without 47988 itself that is 80140, so 47988 is abundant (80140 is more than 47988). Euler's totient φ(47988) = 15120 numbers up to 47988 share no factor with it.
- 4
The digits of 47988 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47988 = 2^{2} \times 3^{2} \times 31 \times 43 \]47988 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 128128 |
| Euler totient φ(n) | 15120 |
| Square | 2302848144 |
| Cube | 110509076734272 |
| Square root | 219.061635 (= 6√1333) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 52 |
| Scientific notation | 4.7988 × |
47988 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand nine hundred and eighty-eight |
| Binary (base 2) | 1011101101110100 |
| Octal (base 8) | 135564 |
| Hexadecimal (base 16) | BB74 |
| Base 3 | 2102211100 |
| As time | 47988 seconds = 13 h 19 min 48 s |
Is 47988 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47988 ÷ 2 = 23994) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (47988 ÷ 3 = 15996) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47988 ÷ 4 = 11997) | 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 (47988 ÷ 6 = 7998) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (47988 ÷ 9 = 5332) | 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 (47988 ÷ 12 = 3999) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47988 a prime number?
No. 47988 = × × 31 × 43, so it is divisible by 2.
What are the factors of 47988?
1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 43, 62, 86, 93, 124, 129, 172, 186, 258, 279, 372, 387, 516, 558, 774, 1116, 1333, 1548, 2666, 3999, 5332, 7998, 11997, 15996, 23994, 47988.
What is 47988 in binary?
1011101101110100 (hexadecimal BB74, octal 135564).
What is the square root of 47988?
About 219.0616, exactly 6√1333.
Is 47988 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 47988?
47988 is a Harshad number: divisible by its digit sum 36.