The number 16416
16416 is a composite number with 48 divisors. Its prime factorisation is × × 19. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 32, 36, 38 … 16416.
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How to work it out
- 1
What is special about 16416: a Harshad number: divisible by its digit sum 18.
- 2
16416 is composite. Its prime factorisation is
- 3
The divisors add up to 50400; without 16416 itself that is 33984, so 16416 is abundant (33984 is more than 16416). Euler's totient φ(16416) = 5184 numbers up to 16416 share no factor with it.
- 4
The digits of 16416 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 16416 = 2^{5} \times 3^{3} \times 19 \]16416 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 50400 |
| Euler totient φ(n) | 5184 |
| Square | 269485056 |
| Cube | 4423866679296 |
| Square root | 128.124939 (= 12√114) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 40 |
| Scientific notation | 1.6416 × |
16416 in other forms
| Form | Value |
|---|---|
| In words | sixteen thousand four hundred and sixteen |
| Binary (base 2) | 100000000100000 |
| Octal (base 8) | 40040 |
| Hexadecimal (base 16) | 4020 |
| Base 3 | 211112000 |
| As time | 16416 seconds = 4 h 33 min 36 s |
Is 16416 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (16416 ÷ 2 = 8208) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (16416 ÷ 3 = 5472) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (16416 ÷ 4 = 4104) | 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 (16416 ÷ 6 = 2736) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (16416 ÷ 8 = 2052) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (16416 ÷ 9 = 1824) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (16416 ÷ 12 = 1368) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 16416 a prime number?
No. 16416 = × × 19, so it is divisible by 2.
What are the factors of 16416?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 32, 36, 38, 48, 54, 57, 72, 76, 96, 108, 114, 144, 152, 171, 216, 228, 288, 304, 342, 432, 456, 513, 608, 684, 864, 912, 1026, 1368, 1824, 2052, 2736, 4104, 5472, 8208, 16416.
What is 16416 in binary?
100000000100000 (hexadecimal 4020, octal 40040).
What is the square root of 16416?
About 128.1249, exactly 12√114.
Is 16416 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 16416?
16416 is a Harshad number: divisible by its digit sum 18.