The number 21456
21456 is a composite number with 30 divisors. Its prime factorisation is × × 149. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 149 … 21456.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21456: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
21456 is composite. Its prime factorisation is
- 3
The divisors add up to 60450; without 21456 itself that is 38994, so 21456 is abundant (38994 is more than 21456). Euler's totient φ(21456) = 7104 numbers up to 21456 share no factor with it.
- 4
The digits of 21456 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 74 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21456 = 2^{4} \times 3^{2} \times 149 \]21456 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 60450 |
| Euler totient φ(n) | 7104 |
| Square | 460359936 |
| Cube | 9877482786816 |
| Square root | 146.478667 (= 12√149) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 74 |
| Scientific notation | 2.1456 × |
21456 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand four hundred and fifty-six |
| Binary (base 2) | 101001111010000 |
| Octal (base 8) | 51720 |
| Hexadecimal (base 16) | 53D0 |
| Base 3 | 1002102200 |
| As time | 21456 seconds = 5 h 57 min 36 s |
Is 21456 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21456 ÷ 2 = 10728) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21456 ÷ 3 = 7152) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21456 ÷ 4 = 5364) | 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 (21456 ÷ 6 = 3576) | 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 (21456 ÷ 8 = 2682) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (21456 ÷ 9 = 2384) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21456 ÷ 12 = 1788) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21456 a prime number?
No. 21456 = × × 149, so it is divisible by 2.
What are the factors of 21456?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 149, 298, 447, 596, 894, 1192, 1341, 1788, 2384, 2682, 3576, 5364, 7152, 10728, 21456.
What is 21456 in binary?
101001111010000 (hexadecimal 53D0, octal 51720).
What is the square root of 21456?
About 146.4787, exactly 12√149.
Is 21456 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 21456?
21456 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.