The number 9750
9750 is a composite number with 32 divisors. Its prime factorisation is 2 × 3 × × 13. Divisors (32): 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78 … 9750.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
9750 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
9750 is composite. Its prime factorisation is
- 3
The divisors add up to 26208; without 9750 itself that is 16458, so 9750 is abundant (16458 is more than 9750). Euler's totient φ(9750) = 2400 numbers up to 9750 share no factor with it.
- 4
The digits of 9750 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 122 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9750 = 2 \times 3 \times 5^{3} \times 13 \]9750 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 26208 |
| Euler totient φ(n) | 2400 |
| Square | 95062500 |
| Cube | 926859375000 |
| Square root | 98.742088 (= 5√390) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 122 |
| Scientific notation | 9.75 × |
9750 in other forms
| Form | Value |
|---|---|
| In words | nine thousand seven hundred and fifty |
| Binary (base 2) | 10011000010110 |
| Octal (base 8) | 23026 |
| Hexadecimal (base 16) | 2616 |
| Base 3 | 111101010 |
| As time | 9750 seconds = 2 h 42 min 30 s |
Is 9750 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9750 ÷ 2 = 4875) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9750 ÷ 3 = 3250) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9750 ÷ 5 = 1950) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9750 ÷ 6 = 1625) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 6) | 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 | Yes (9750 ÷ 10 = 975) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9750 a prime number?
No. 9750 = 2 × 3 × × 13, so it is divisible by 2.
What are the factors of 9750?
1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 125, 130, 150, 195, 250, 325, 375, 390, 650, 750, 975, 1625, 1950, 3250, 4875, 9750.
What is 9750 in binary?
10011000010110 (hexadecimal 2616, octal 23026).
What is the square root of 9750?
About 98.7421, exactly 5√390.
Is 9750 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 9750?
It is a composite number with 32 divisors.