The number 20961
20961 is a composite number with 12 divisors. Its prime factorisation is × 17 × 137. Divisors (12): 1, 3, 9, 17, 51, 137, 153, 411, 1233, 2329, 6987, 20961.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
20961 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
20961 is composite. Its prime factorisation is
- 3
The divisors add up to 32292; without 20961 itself that is 11331, so 20961 is deficient (11331 is less than 20961). Euler's totient φ(20961) = 13056 numbers up to 20961 share no factor with it.
- 4
The digits of 20961 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 87 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20961 = 3^{2} \times 17 \times 137 \]20961 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 32292 |
| Euler totient φ(n) | 13056 |
| Square | 439363521 |
| Cube | 9209498763681 |
| Square root | 144.779142 (= 3√2329) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 87 |
| Scientific notation | 2.0961 × |
20961 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand nine hundred and sixty-one |
| Binary (base 2) | 101000111100001 |
| Octal (base 8) | 50741 |
| Hexadecimal (base 16) | 51E1 |
| Base 3 | 1001202100 |
| As time | 20961 seconds = 5 h 49 min 21 s |
Is 20961 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 | Yes (20961 ÷ 3 = 6987) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | Yes (20961 ÷ 9 = 2329) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20961 a prime number?
No. 20961 = × 17 × 137, so it is divisible by 3.
What are the factors of 20961?
1, 3, 9, 17, 51, 137, 153, 411, 1233, 2329, 6987, 20961.
What is 20961 in binary?
101000111100001 (hexadecimal 51E1, octal 50741).
What is the square root of 20961?
About 144.7791, exactly 3√2329.
Is 20961 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 20961?
It is a composite number with 12 divisors.