The number 12416
12416 is a composite number with 16 divisors. Its prime factorisation is × 97. Divisors (16): 1, 2, 4, 8, 16, 32, 64, 97, 128, 194, 388, 776, 1552, 3104, 6208, 12416.
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How to work it out
- 1
12416 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
12416 is composite. Its prime factorisation is
- 3
The divisors add up to 24990; without 12416 itself that is 12574, so 12416 is abundant (12574 is more than 12416). Euler's totient φ(12416) = 6144 numbers up to 12416 share no factor with it.
- 4
The digits of 12416 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12416 = 2^{7} \times 97 \]12416 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 24990 |
| Euler totient φ(n) | 6144 |
| Square | 154157056 |
| Cube | 1914014007296 |
| Square root | 111.427106 (= 8√194) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 125 |
| Scientific notation | 1.2416 × |
12416 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand four hundred and sixteen |
| Binary (base 2) | 11000010000000 |
| Octal (base 8) | 30200 |
| Hexadecimal (base 16) | 3080 |
| Base 3 | 122000212 |
| As time | 12416 seconds = 3 h 26 min 56 s |
Is 12416 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12416 ÷ 2 = 6208) | 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 (12416 ÷ 4 = 3104) | 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 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 (12416 ÷ 8 = 1552) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 8) | 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 12416 a prime number?
No. 12416 = × 97, so it is divisible by 2.
What are the factors of 12416?
1, 2, 4, 8, 16, 32, 64, 97, 128, 194, 388, 776, 1552, 3104, 6208, 12416.
What is 12416 in binary?
11000010000000 (hexadecimal 3080, octal 30200).
What is the square root of 12416?
About 111.4271, exactly 8√194.
Is 12416 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 12416?
It is a composite number with 16 divisors.