The number 27408
27408 is a composite number with 20 divisors. Its prime factorisation is × 3 × 571. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 571, 1142, 1713, 2284, 3426, 4568 … 27408.
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How to work it out
- 1
What is special about 27408: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
27408 is composite. Its prime factorisation is
- 3
The divisors add up to 70928; without 27408 itself that is 43520, so 27408 is abundant (43520 is more than 27408). Euler's totient φ(27408) = 9120 numbers up to 27408 share no factor with it.
- 4
The digits of 27408 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 33 steps to reach 1.
LaTeX source of the formulas on this page
\[ 27408 = 2^{4} \times 3 \times 571 \]27408 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 70928 |
| Euler totient φ(n) | 9120 |
| Square | 751198464 |
| Cube | 20588847501312 |
| Square root | 165.553617 (= 4√1713) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 33 |
| Scientific notation | 2.7408 × |
27408 in other forms
| Form | Value |
|---|---|
| In words | twenty-seven thousand four hundred and eight |
| Binary (base 2) | 110101100010000 |
| Octal (base 8) | 65420 |
| Hexadecimal (base 16) | 6B10 |
| Base 3 | 1101121010 |
| As time | 27408 seconds = 7 h 36 min 48 s |
Is 27408 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (27408 ÷ 2 = 13704) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (27408 ÷ 3 = 9136) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (27408 ÷ 4 = 6852) | 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 (27408 ÷ 6 = 4568) | 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 | Yes (27408 ÷ 8 = 3426) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (27408 ÷ 12 = 2284) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 27408 a prime number?
No. 27408 = × 3 × 571, so it is divisible by 2.
What are the factors of 27408?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 571, 1142, 1713, 2284, 3426, 4568, 6852, 9136, 13704, 27408.
What is 27408 in binary?
110101100010000 (hexadecimal 6B10, octal 65420).
What is the square root of 27408?
About 165.5536, exactly 4√1713.
Is 27408 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 27408?
27408 is a happy number: repeatedly adding the squares of its digits reaches 1.