The number 9801
9801 is a perfect square (99²). Its prime factorisation is × . Divisors (15): 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9801: a perfect square (99²).
- 2
9801 is composite. Its prime factorisation is
- 3
The divisors add up to 16093; without 9801 itself that is 6292, so 9801 is deficient (6292 is less than 9801). Euler's totient φ(9801) = 5940 numbers up to 9801 share no factor with it.
- 4
The digits of 9801 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 104 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9801 = 3^{4} \times 11^{2} \]9801 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 15 |
| Sum of divisors | 16093 |
| Euler totient φ(n) | 5940 |
| Square | 96059601 |
| Cube | 941480149401 |
| Square root | 99 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 104 |
| Scientific notation | 9.801 × |
| Perfect power |
9801 in other forms
| Form | Value |
|---|---|
| In words | nine thousand eight hundred and one |
| Binary (base 2) | 10011001001001 |
| Octal (base 8) | 23111 |
| Hexadecimal (base 16) | 2649 |
| Base 3 | 111110000 |
| As time | 9801 seconds = 2 h 43 min 21 s |
Is 9801 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 (9801 ÷ 3 = 3267) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9801 ÷ 9 = 1089) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (9801 ÷ 11 = 891) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9801 a prime number?
No. 9801 = × , so it is divisible by 3.
What are the factors of 9801?
1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.
What is 9801 in binary?
10011001001001 (hexadecimal 2649, octal 23111).
What is the square root of 9801?
99, because 99 × 99 = 9801.
Is 9801 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 9801?
9801 is a perfect square (99²).