The number 960
960 is a composite number with 28 divisors. Its prime factorisation is × 3 × 5. Divisors (28): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 960.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 960: a Harshad number: divisible by its digit sum 15.
- 2
960 is composite. Its prime factorisation is
- 3
The divisors add up to 3048; without 960 itself that is 2088, so 960 is abundant (2088 is more than 960). Euler's totient φ(960) = 256 numbers up to 960 share no factor with it.
- 4
The digits of 960 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 23 steps to reach 1.
LaTeX source of the formulas on this page
\[ 960 = 2^{6} \times 3 \times 5 \]960 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 3048 |
| Euler totient φ(n) | 256 |
| Square | 921600 |
| Cube | 884736000 |
| Square root | 30.983867 (= 8√15) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 23 |
| Scientific notation | 9.6 × |
960 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and sixty |
| Roman numerals | CMLX |
| Binary (base 2) | 1111000000 |
| Octal (base 8) | 1700 |
| Hexadecimal (base 16) | 3C0 |
| Base 3 | 1022120 |
| As time | 960 seconds = 16 min 0 s |
Is 960 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (960 ÷ 2 = 480) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (960 ÷ 3 = 320) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (960 ÷ 4 = 240) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (960 ÷ 5 = 192) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (960 ÷ 6 = 160) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (960 ÷ 8 = 120) | 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 (960 ÷ 10 = 96) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (960 ÷ 12 = 80) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 960 a prime number?
No. 960 = × 3 × 5, so it is divisible by 2.
What are the factors of 960?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960.
What is 960 in binary?
1111000000 (hexadecimal 3C0, octal 1700).
What is the square root of 960?
About 30.9839, exactly 8√15.
What is 960 in Roman numerals?
CMLX.
Is 960 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 960?
960 is a Harshad number: divisible by its digit sum 15.