The number 961
961 is a perfect square (31²). Its prime factorisation is . Divisors (3): 1, 31, 961.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 961: a perfect square (31²); the square of a prime (31²).
- 2
961 is composite. Its prime factorisation is
- 3
The divisors add up to 993; without 961 itself that is 32, so 961 is deficient (32 is less than 961). Euler's totient φ(961) = 930 numbers up to 961 share no factor with it.
- 4
The digits of 961 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 961 = 31^{2} \]961 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 3 |
| Sum of divisors | 993 |
| Euler totient φ(n) | 930 |
| Square | 923521 |
| Cube | 887503681 |
| Square root | 31 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 49 |
| Scientific notation | 9.61 × |
| Perfect power |
961 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and sixty-one |
| Roman numerals | CMLXI |
| Binary (base 2) | 1111000001 |
| Octal (base 8) | 1701 |
| Hexadecimal (base 16) | 3C1 |
| Base 3 | 1022121 |
| As time | 961 seconds = 16 min 1 s |
Is 961 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 961 a prime number?
No. 961 = , so it is divisible by 31.
What are the factors of 961?
1, 31, 961.
What is 961 in binary?
1111000001 (hexadecimal 3C1, octal 1701).
What is the square root of 961?
31, because 31 × 31 = 961.
What is 961 in Roman numerals?
CMLXI.
Is 961 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 961?
961 is a perfect square (31²); the square of a prime (31²).