The number 966
966 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 7 × 23. Divisors (16): 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 966: a Harshad number: divisible by its digit sum 21.
- 2
966 is composite. Its prime factorisation is
- 3
The divisors add up to 2304; without 966 itself that is 1338, so 966 is abundant (1338 is more than 966). Euler's totient φ(966) = 264 numbers up to 966 share no factor with it.
- 4
The digits of 966 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 23 steps to reach 1.
LaTeX source of the formulas on this page
\[ 966 = 2 \times 3 \times 7 \times 23 \]
966 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 2304 |
| Euler totient φ(n) | 264 |
| Square | 933156 |
| Cube | 901428696 |
| Square root | 31.080541 |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 23 |
| Scientific notation | 9.66 × |
966 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and sixty-six |
| Roman numerals | CMLXVI |
| Binary (base 2) | 1111000110 |
| Octal (base 8) | 1706 |
| Hexadecimal (base 16) | 3C6 |
| Base 3 | 1022210 |
| As time | 966 seconds = 16 min 6 s |
Is 966 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (966 ÷ 2 = 483) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (966 ÷ 3 = 322) | 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 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (966 ÷ 6 = 161) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (966 ÷ 7 = 138) | 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 | No (remainder 6) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 966 a prime number?
No. 966 = 2 × 3 × 7 × 23, so it is divisible by 2.
What are the factors of 966?
1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966.
What is 966 in binary?
1111000110 (hexadecimal 3C6, octal 1706).
What is the square root of 966?
About 31.0805.
What is 966 in Roman numerals?
CMLXVI.
Is 966 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 966?
966 is a Harshad number: divisible by its digit sum 21.