The number 9720
9720 is a composite number with 48 divisors. Its prime factorisation is × × 5. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30 … 9720.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9720: a Harshad number: divisible by its digit sum 18.
- 2
9720 is composite. Its prime factorisation is
- 3
The divisors add up to 32760; without 9720 itself that is 23040, so 9720 is abundant (23040 is more than 9720). Euler's totient φ(9720) = 2592 numbers up to 9720 share no factor with it.
- 4
The digits of 9720 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 166 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9720 = 2^{3} \times 3^{5} \times 5 \]9720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 32760 |
| Euler totient φ(n) | 2592 |
| Square | 94478400 |
| Cube | 918330048000 |
| Square root | 98.590060 (= 18√30) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 166 |
| Scientific notation | 9.72 × |
9720 in other forms
| Form | Value |
|---|---|
| In words | nine thousand seven hundred and twenty |
| Binary (base 2) | 10010111111000 |
| Octal (base 8) | 22770 |
| Hexadecimal (base 16) | 25F8 |
| Base 3 | 111100000 |
| As time | 9720 seconds = 2 h 42 min 0 s |
Is 9720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9720 ÷ 2 = 4860) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9720 ÷ 3 = 3240) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9720 ÷ 4 = 2430) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9720 ÷ 5 = 1944) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9720 ÷ 6 = 1620) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 | Yes (9720 ÷ 8 = 1215) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (9720 ÷ 9 = 1080) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (9720 ÷ 10 = 972) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9720 ÷ 12 = 810) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9720 a prime number?
No. 9720 = × × 5, so it is divisible by 2.
What are the factors of 9720?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 243, 270, 324, 360, 405, 486, 540, 648, 810, 972, 1080, 1215, 1620, 1944, 2430, 3240, 4860, 9720.
What is 9720 in binary?
10010111111000 (hexadecimal 25F8, octal 22770).
What is the square root of 9720?
About 98.5901, exactly 18√30.
Is 9720 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 9720?
9720 is a Harshad number: divisible by its digit sum 18.