The number 40416
40416 is a composite number with 24 divisors. Its prime factorisation is × 3 × 421. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 421, 842, 1263, 1684 … 40416.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
40416 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
40416 is composite. Its prime factorisation is
- 3
The divisors add up to 106344; without 40416 itself that is 65928, so 40416 is abundant (65928 is more than 40416). Euler's totient φ(40416) = 13440 numbers up to 40416 share no factor with it.
- 4
The digits of 40416 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 181 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40416 = 2^{5} \times 3 \times 421 \]40416 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 106344 |
| Euler totient φ(n) | 13440 |
| Square | 1633453056 |
| Cube | 66017638711296 |
| Square root | 201.037310 (= 4√2526) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 181 |
| Scientific notation | 4.0416 × |
40416 in other forms
| Form | Value |
|---|---|
| In words | forty thousand four hundred and sixteen |
| Binary (base 2) | 1001110111100000 |
| Octal (base 8) | 116740 |
| Hexadecimal (base 16) | 9DE0 |
| Base 3 | 2001102220 |
| As time | 40416 seconds = 11 h 13 min 36 s |
Is 40416 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40416 ÷ 2 = 20208) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (40416 ÷ 3 = 13472) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40416 ÷ 4 = 10104) | 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 (40416 ÷ 6 = 6736) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (40416 ÷ 8 = 5052) | 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 6) | 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 (40416 ÷ 12 = 3368) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40416 a prime number?
No. 40416 = × 3 × 421, so it is divisible by 2.
What are the factors of 40416?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 421, 842, 1263, 1684, 2526, 3368, 5052, 6736, 10104, 13472, 20208, 40416.
What is 40416 in binary?
1001110111100000 (hexadecimal 9DE0, octal 116740).
What is the square root of 40416?
About 201.0373, exactly 4√2526.
Is 40416 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 40416?
It is a composite number with 24 divisors.