The number 21736
21736 is a triangular number: 1 + 2 + … + 208 = 21736. Its prime factorisation is × 11 × 13 × 19. Divisors (32): 1, 2, 4, 8, 11, 13, 19, 22, 26, 38, 44, 52, 76, 88, 104, 143 … 21736.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21736: a triangular number: 1 + 2 + … + 208 = 21736; a Harshad number: divisible by its digit sum 19.
- 2
21736 is composite. Its prime factorisation is
- 3
The divisors add up to 50400; without 21736 itself that is 28664, so 21736 is abundant (28664 is more than 21736). Euler's totient φ(21736) = 8640 numbers up to 21736 share no factor with it.
- 4
The digits of 21736 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 69 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21736 = 2^{3} \times 11 \times 13 \times 19 \]21736 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 50400 |
| Euler totient φ(n) | 8640 |
| Square | 472453696 |
| Cube | 10269253536256 |
| Square root | 147.431340 (= 2√5434) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 69 |
| Scientific notation | 2.1736 × |
21736 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand seven hundred and thirty-six |
| Binary (base 2) | 101010011101000 |
| Octal (base 8) | 52350 |
| Hexadecimal (base 16) | 54E8 |
| Base 3 | 1002211001 |
| As time | 21736 seconds = 6 h 2 min 16 s |
Is 21736 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21736 ÷ 2 = 10868) | 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 | Yes (21736 ÷ 4 = 5434) | 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 4) | 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 (21736 ÷ 8 = 2717) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | 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 | Yes (21736 ÷ 11 = 1976) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21736 a prime number?
No. 21736 = × 11 × 13 × 19, so it is divisible by 2.
What are the factors of 21736?
1, 2, 4, 8, 11, 13, 19, 22, 26, 38, 44, 52, 76, 88, 104, 143, 152, 209, 247, 286, 418, 494, 572, 836, 988, 1144, 1672, 1976, 2717, 5434, 10868, 21736.
What is 21736 in binary?
101010011101000 (hexadecimal 54E8, octal 52350).
What is the square root of 21736?
About 147.4313, exactly 2√5434.
Is 21736 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 21736?
21736 is a triangular number: 1 + 2 + … + 208 = 21736; a Harshad number: divisible by its digit sum 19.