The number 9900
9900 is a composite number with 54 divisors. Its prime factorisation is × × × 11. Divisors (54): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30 … 9900.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9900: a Harshad number: divisible by its digit sum 18.
- 2
9900 is composite. Its prime factorisation is
- 3
The divisors add up to 33852; without 9900 itself that is 23952, so 9900 is abundant (23952 is more than 9900). Euler's totient φ(9900) = 2400 numbers up to 9900 share no factor with it.
- 4
The digits of 9900 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 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9900 = 2^{2} \times 3^{2} \times 5^{2} \times 11 \]9900 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 54 |
| Sum of divisors | 33852 |
| Euler totient φ(n) | 2400 |
| Square | 98010000 |
| Cube | 970299000000 |
| Square root | 99.498744 (= 30√11) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 73 |
| Scientific notation | 9.9 × |
9900 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred |
| Binary (base 2) | 10011010101100 |
| Octal (base 8) | 23254 |
| Hexadecimal (base 16) | 26AC |
| Base 3 | 111120200 |
| As time | 9900 seconds = 2 h 45 min 0 s |
Is 9900 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9900 ÷ 2 = 4950) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9900 ÷ 3 = 3300) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9900 ÷ 4 = 2475) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9900 ÷ 5 = 1980) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9900 ÷ 6 = 1650) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (9900 ÷ 9 = 1100) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (9900 ÷ 10 = 990) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (9900 ÷ 11 = 900) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9900 ÷ 12 = 825) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9900 a prime number?
No. 9900 = × × × 11, so it is divisible by 2.
What are the factors of 9900?
1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300, 4950, 9900.
What is 9900 in binary?
10011010101100 (hexadecimal 26AC, octal 23254).
What is the square root of 9900?
About 99.4987, exactly 30√11.
Is 9900 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 9900?
9900 is a Harshad number: divisible by its digit sum 18.