The number 9975
9975 is a composite number with 24 divisors. Its prime factorisation is 3 × × 7 × 19. Divisors (24): 1, 3, 5, 7, 15, 19, 21, 25, 35, 57, 75, 95, 105, 133, 175, 285 … 9975.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9975: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
9975 is composite. Its prime factorisation is
- 3
The divisors add up to 19840; without 9975 itself that is 9865, so 9975 is deficient (9865 is less than 9975). Euler's totient φ(9975) = 4320 numbers up to 9975 share no factor with it.
- 4
The digits of 9975 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 166 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9975 = 3 \times 5^{2} \times 7 \times 19 \]9975 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 19840 |
| Euler totient φ(n) | 4320 |
| Square | 99500625 |
| Cube | 992518734375 |
| Square root | 99.874922 (= 5√399) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 166 |
| Scientific notation | 9.975 × |
9975 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and seventy-five |
| Binary (base 2) | 10011011110111 |
| Octal (base 8) | 23367 |
| Hexadecimal (base 16) | 26F7 |
| Base 3 | 111200110 |
| As time | 9975 seconds = 2 h 46 min 15 s |
Is 9975 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 (9975 ÷ 3 = 3325) | 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 | Yes (9975 ÷ 5 = 1995) | 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 | Yes (9975 ÷ 7 = 1425) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 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 9975 a prime number?
No. 9975 = 3 × × 7 × 19, so it is divisible by 3.
What are the factors of 9975?
1, 3, 5, 7, 15, 19, 21, 25, 35, 57, 75, 95, 105, 133, 175, 285, 399, 475, 525, 665, 1425, 1995, 3325, 9975.
What is 9975 in binary?
10011011110111 (hexadecimal 26F7, octal 23367).
What is the square root of 9975?
About 99.8749, exactly 5√399.
Is 9975 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 9975?
9975 is a happy number: repeatedly adding the squares of its digits reaches 1.