The number 99
99 is a palindrome: it reads 99 backwards too and a binary palindrome (1100011). Its prime factorisation is × 11. Divisors (6): 1, 3, 9, 11, 33, 99.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 99: a palindrome: it reads 99 backwards too; a binary palindrome (1100011).
- 2
99 is composite. Its prime factorisation is
- 3
The divisors add up to 156; without 99 itself that is 57, so 99 is deficient (57 is less than 99). Euler's totient φ(99) = 60 numbers up to 99 share no factor with it.
- 4
The digits of 99 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 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 99 = 3^{2} \times 11 \]99 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 156 |
| Euler totient φ(n) | 60 |
| Square | 9801 |
| Cube | 970299 |
| Square root | 9.949874 (= 3√11) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 25 |
| Scientific notation | 9.9 × |
99 in other forms
| Form | Value |
|---|---|
| In words | ninety-nine |
| Roman numerals | XCIX |
| Binary (base 2) | 1100011 |
| Octal (base 8) | 143 |
| Hexadecimal (base 16) | 63 |
| Base 3 | 10200 |
| As time | 99 seconds = 1 min 39 s |
Is 99 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (99 ÷ 3 = 33) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (99 ÷ 9 = 11) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (99 ÷ 11 = 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 99 a prime number?
No. 99 = × 11, so it is divisible by 3.
What are the factors of 99?
1, 3, 9, 11, 33, 99.
What is 99 in binary?
1100011 (hexadecimal 63, octal 143).
What is the square root of 99?
About 9.9499, exactly 3√11.
What is 99 in Roman numerals?
XCIX.
Is 99 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 99?
99 is a palindrome: it reads 99 backwards too; a binary palindrome (1100011).