The number 91988
91988 is a composite number with 24 divisors. Its prime factorisation is × 13 × 29 × 61. Divisors (24): 1, 2, 4, 13, 26, 29, 52, 58, 61, 116, 122, 244, 377, 754, 793, 1508 … 91988.
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How to work it out
- 1
What is special about 91988: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
91988 is composite. Its prime factorisation is
- 3
The divisors add up to 182280; without 91988 itself that is 90292, so 91988 is deficient (90292 is less than 91988). Euler's totient φ(91988) = 40320 numbers up to 91988 share no factor with it.
- 4
The digits of 91988 add up to 35, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.
LaTeX source of the formulas on this page
\[ 91988 = 2^{2} \times 13 \times 29 \times 61 \]91988 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 182280 |
| Euler totient φ(n) | 40320 |
| Square | 8461792144 |
| Cube | 778383335742272 |
| Square root | 303.295236 (= 2√22997) |
| Digit sum / digital root | 35 / 8 |
| Collatz steps to 1 | 58 |
| Scientific notation | 9.1988 × |
91988 in other forms
| Form | Value |
|---|---|
| In words | ninety-one thousand nine hundred and eighty-eight |
| Binary (base 2) | 10110011101010100 |
| Octal (base 8) | 263524 |
| Hexadecimal (base 16) | 16754 |
| Base 3 | 11200011222 |
| As time | 91988 seconds = 25 h 33 min 8 s |
Is 91988 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (91988 ÷ 2 = 45994) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (91988 ÷ 4 = 22997) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | No (remainder 8) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 91988 a prime number?
No. 91988 = × 13 × 29 × 61, so it is divisible by 2.
What are the factors of 91988?
1, 2, 4, 13, 26, 29, 52, 58, 61, 116, 122, 244, 377, 754, 793, 1508, 1586, 1769, 3172, 3538, 7076, 22997, 45994, 91988.
What is 91988 in binary?
10110011101010100 (hexadecimal 16754, octal 263524).
What is the square root of 91988?
About 303.2952, exactly 2√22997.
Is 91988 divisible by 3?
No. Its digits add up to 35, which is not a multiple of 3.
What is special about the number 91988?
91988 is a happy number: repeatedly adding the squares of its digits reaches 1.