The number 416
416 is a composite number with 12 divisors. Its prime factorisation is × 13. Divisors (12): 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
416 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
416 is composite. Its prime factorisation is
- 3
The divisors add up to 882; without 416 itself that is 466, so 416 is abundant (466 is more than 416). Euler's totient φ(416) = 192 numbers up to 416 share no factor with it.
- 4
The digits of 416 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 14 steps to reach 1.
LaTeX source of the formulas on this page
\[ 416 = 2^{5} \times 13 \]416 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 882 |
| Euler totient φ(n) | 192 |
| Square | 173056 |
| Cube | 71991296 |
| Square root | 20.396078 (= 4√26) |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 14 |
| Scientific notation | 4.16 × |
416 in other forms
| Form | Value |
|---|---|
| In words | four hundred and sixteen |
| Roman numerals | CDXVI |
| Binary (base 2) | 110100000 |
| Octal (base 8) | 640 |
| Hexadecimal (base 16) | 1A0 |
| Base 3 | 120102 |
| As time | 416 seconds = 6 min 56 s |
Is 416 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (416 ÷ 2 = 208) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (416 ÷ 4 = 104) | 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 2) | 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 (416 ÷ 8 = 52) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 416 a prime number?
No. 416 = × 13, so it is divisible by 2.
What are the factors of 416?
1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416.
What is 416 in binary?
110100000 (hexadecimal 1A0, octal 640).
What is the square root of 416?
About 20.3961, exactly 4√26.
What is 416 in Roman numerals?
CDXVI.
Is 416 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 416?
It is a composite number with 12 divisors.