The number 9990
9990 is a composite number with 32 divisors. Its prime factorisation is 2 × × 5 × 37. Divisors (32): 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 37, 45, 54, 74, 90 … 9990.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9990: a Harshad number: divisible by its digit sum 27.
- 2
9990 is composite. Its prime factorisation is
- 3
The divisors add up to 27360; without 9990 itself that is 17370, so 9990 is abundant (17370 is more than 9990). Euler's totient φ(9990) = 2592 numbers up to 9990 share no factor with it.
- 4
The digits of 9990 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 91 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9990 = 2 \times 3^{3} \times 5 \times 37 \]9990 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 27360 |
| Euler totient φ(n) | 2592 |
| Square | 99800100 |
| Cube | 997002999000 |
| Square root | 99.949987 (= 3√1110) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 91 |
| Scientific notation | 9.99 × |
9990 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and ninety |
| Binary (base 2) | 10011100000110 |
| Octal (base 8) | 23406 |
| Hexadecimal (base 16) | 2706 |
| Base 3 | 111201000 |
| As time | 9990 seconds = 2 h 46 min 30 s |
Is 9990 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9990 ÷ 2 = 4995) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9990 ÷ 3 = 3330) | 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 | Yes (9990 ÷ 5 = 1998) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9990 ÷ 6 = 1665) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9990 ÷ 9 = 1110) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (9990 ÷ 10 = 999) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9990 a prime number?
No. 9990 = 2 × × 5 × 37, so it is divisible by 2.
What are the factors of 9990?
1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 37, 45, 54, 74, 90, 111, 135, 185, 222, 270, 333, 370, 555, 666, 999, 1110, 1665, 1998, 3330, 4995, 9990.
What is 9990 in binary?
10011100000110 (hexadecimal 2706, octal 23406).
What is the square root of 9990?
About 99.9500, exactly 3√1110.
Is 9990 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 9990?
9990 is a Harshad number: divisible by its digit sum 27.