The number 21408
21408 is a composite number with 24 divisors. Its prime factorisation is × 3 × 223. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 223, 446, 669, 892 … 21408.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
21408 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
21408 is composite. Its prime factorisation is
- 3
The divisors add up to 56448; without 21408 itself that is 35040, so 21408 is abundant (35040 is more than 21408). Euler's totient φ(21408) = 7104 numbers up to 21408 share no factor with it.
- 4
The digits of 21408 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 74 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21408 = 2^{5} \times 3 \times 223 \]21408 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 56448 |
| Euler totient φ(n) | 7104 |
| Square | 458302464 |
| Cube | 9811339149312 |
| Square root | 146.314729 (= 4√1338) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 74 |
| Scientific notation | 2.1408 × |
21408 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand four hundred and eight |
| Binary (base 2) | 101001110100000 |
| Octal (base 8) | 51640 |
| Hexadecimal (base 16) | 53A0 |
| Base 3 | 1002100220 |
| As time | 21408 seconds = 5 h 56 min 48 s |
Is 21408 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21408 ÷ 2 = 10704) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21408 ÷ 3 = 7136) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21408 ÷ 4 = 5352) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21408 ÷ 6 = 3568) | 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 | Yes (21408 ÷ 8 = 2676) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21408 ÷ 12 = 1784) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21408 a prime number?
No. 21408 = × 3 × 223, so it is divisible by 2.
What are the factors of 21408?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 223, 446, 669, 892, 1338, 1784, 2676, 3568, 5352, 7136, 10704, 21408.
What is 21408 in binary?
101001110100000 (hexadecimal 53A0, octal 51640).
What is the square root of 21408?
About 146.3147, exactly 4√1338.
Is 21408 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 21408?
It is a composite number with 24 divisors.