The number 9945
9945 is a binary palindrome (10011011011001). Its prime factorisation is × 5 × 13 × 17. Divisors (24): 1, 3, 5, 9, 13, 15, 17, 39, 45, 51, 65, 85, 117, 153, 195, 221 … 9945.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9945: a binary palindrome (10011011011001); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
9945 is composite. Its prime factorisation is
- 3
The divisors add up to 19656; without 9945 itself that is 9711, so 9945 is deficient (9711 is less than 9945). Euler's totient φ(9945) = 4608 numbers up to 9945 share no factor with it.
- 4
The digits of 9945 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 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9945 = 3^{2} \times 5 \times 13 \times 17 \]9945 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 19656 |
| Euler totient φ(n) | 4608 |
| Square | 98903025 |
| Cube | 983590583625 |
| Square root | 99.724621 (= 3√1105) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 73 |
| Scientific notation | 9.945 × |
9945 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and forty-five |
| Binary (base 2) | 10011011011001 |
| Octal (base 8) | 23331 |
| Hexadecimal (base 16) | 26D9 |
| Base 3 | 111122100 |
| As time | 9945 seconds = 2 h 45 min 45 s |
Is 9945 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 (9945 ÷ 3 = 3315) | 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 | Yes (9945 ÷ 5 = 1989) | 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 5) | 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 (9945 ÷ 9 = 1105) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 9945 a prime number?
No. 9945 = × 5 × 13 × 17, so it is divisible by 3.
What are the factors of 9945?
1, 3, 5, 9, 13, 15, 17, 39, 45, 51, 65, 85, 117, 153, 195, 221, 255, 585, 663, 765, 1105, 1989, 3315, 9945.
What is 9945 in binary?
10011011011001 (hexadecimal 26D9, octal 23331).
What is the square root of 9945?
About 99.7246, exactly 3√1105.
Is 9945 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 9945?
9945 is a binary palindrome (10011011011001); a happy number: repeatedly adding the squares of its digits reaches 1.