The number 990
990 is a triangular number: 1 + 2 + … + 44 = 990. Its prime factorisation is 2 × × 5 × 11. Divisors (24): 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66 … 990.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 990: a triangular number: 1 + 2 + … + 44 = 990; a Harshad number: divisible by its digit sum 18.
- 2
990 is composite. Its prime factorisation is
- 3
The divisors add up to 2808; without 990 itself that is 1818, so 990 is abundant (1818 is more than 990). Euler's totient φ(990) = 240 numbers up to 990 share no factor with it.
- 4
The digits of 990 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 98 steps to reach 1.
LaTeX source of the formulas on this page
\[ 990 = 2 \times 3^{2} \times 5 \times 11 \]990 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 2808 |
| Euler totient φ(n) | 240 |
| Square | 980100 |
| Cube | 970299000 |
| Square root | 31.464265 (= 3√110) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 98 |
| Scientific notation | 9.9 × |
990 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and ninety |
| Roman numerals | CMXC |
| Binary (base 2) | 1111011110 |
| Octal (base 8) | 1736 |
| Hexadecimal (base 16) | 3DE |
| Base 3 | 1100200 |
| As time | 990 seconds = 16 min 30 s |
Is 990 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (990 ÷ 2 = 495) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (990 ÷ 3 = 330) | 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 (990 ÷ 5 = 198) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (990 ÷ 6 = 165) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (990 ÷ 9 = 110) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (990 ÷ 10 = 99) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (990 ÷ 11 = 90) | 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 990 a prime number?
No. 990 = 2 × × 5 × 11, so it is divisible by 2.
What are the factors of 990?
1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990.
What is 990 in binary?
1111011110 (hexadecimal 3DE, octal 1736).
What is the square root of 990?
About 31.4643, exactly 3√110.
What is 990 in Roman numerals?
CMXC.
Is 990 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 990?
990 is a triangular number: 1 + 2 + … + 44 = 990; a Harshad number: divisible by its digit sum 18.