The number 9982
9982 is a composite number with 16 divisors. Its prime factorisation is 2 × 7 × 23 × 31. Divisors (16): 1, 2, 7, 14, 23, 31, 46, 62, 161, 217, 322, 434, 713, 1426, 4991, 9982.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9982: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
9982 is composite. Its prime factorisation is
- 3
The divisors add up to 18432; without 9982 itself that is 8450, so 9982 is deficient (8450 is less than 9982). Euler's totient φ(9982) = 3960 numbers up to 9982 share no factor with it.
- 4
The digits of 9982 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9982 = 2 \times 7 \times 23 \times 31 \]
9982 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 18432 |
| Euler totient φ(n) | 3960 |
| Square | 99640324 |
| Cube | 994609714168 |
| Square root | 99.909959 |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 73 |
| Scientific notation | 9.982 × |
9982 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and eighty-two |
| Binary (base 2) | 10011011111110 |
| Octal (base 8) | 23376 |
| Hexadecimal (base 16) | 26FE |
| Base 3 | 111200201 |
| As time | 9982 seconds = 2 h 46 min 22 s |
Is 9982 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9982 ÷ 2 = 4991) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (9982 ÷ 7 = 1426) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9982 a prime number?
No. 9982 = 2 × 7 × 23 × 31, so it is divisible by 2.
What are the factors of 9982?
1, 2, 7, 14, 23, 31, 46, 62, 161, 217, 322, 434, 713, 1426, 4991, 9982.
What is 9982 in binary?
10011011111110 (hexadecimal 26FE, octal 23376).
What is the square root of 9982?
About 99.9100.
Is 9982 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 9982?
9982 is a happy number: repeatedly adding the squares of its digits reaches 1.