The number 9960
9960 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 83. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 83 … 9960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9960: a Harshad number: divisible by its digit sum 24.
- 2
9960 is composite. Its prime factorisation is
- 3
The divisors add up to 30240; without 9960 itself that is 20280, so 9960 is abundant (20280 is more than 9960). Euler's totient φ(9960) = 2624 numbers up to 9960 share no factor with it.
- 4
The digits of 9960 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 91 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9960 = 2^{3} \times 3 \times 5 \times 83 \]9960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 30240 |
| Euler totient φ(n) | 2624 |
| Square | 99201600 |
| Cube | 988047936000 |
| Square root | 99.799800 (= 2√2490) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 91 |
| Scientific notation | 9.96 × |
9960 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and sixty |
| Binary (base 2) | 10011011101000 |
| Octal (base 8) | 23350 |
| Hexadecimal (base 16) | 26E8 |
| Base 3 | 111122220 |
| As time | 9960 seconds = 2 h 46 min 0 s |
Is 9960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9960 ÷ 2 = 4980) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9960 ÷ 3 = 3320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9960 ÷ 4 = 2490) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9960 ÷ 5 = 1992) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9960 ÷ 6 = 1660) | 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 | Yes (9960 ÷ 8 = 1245) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (9960 ÷ 10 = 996) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9960 ÷ 12 = 830) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9960 a prime number?
No. 9960 = × 3 × 5 × 83, so it is divisible by 2.
What are the factors of 9960?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 83, 120, 166, 249, 332, 415, 498, 664, 830, 996, 1245, 1660, 1992, 2490, 3320, 4980, 9960.
What is 9960 in binary?
10011011101000 (hexadecimal 26E8, octal 23350).
What is the square root of 9960?
About 99.7998, exactly 2√2490.
Is 9960 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 9960?
9960 is a Harshad number: divisible by its digit sum 24.