The number 14496
14496 is a composite number with 24 divisors. Its prime factorisation is × 3 × 151. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 151, 302, 453, 604 … 14496.
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How to work it out
- 1
What is special about 14496: a Harshad number: divisible by its digit sum 24.
- 2
14496 is composite. Its prime factorisation is
- 3
The divisors add up to 38304; without 14496 itself that is 23808, so 14496 is abundant (23808 is more than 14496). Euler's totient φ(14496) = 4800 numbers up to 14496 share no factor with it.
- 4
The digits of 14496 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 19 steps to reach 1.
LaTeX source of the formulas on this page
\[ 14496 = 2^{5} \times 3 \times 151 \]14496 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 38304 |
| Euler totient φ(n) | 4800 |
| Square | 210134016 |
| Cube | 3046102695936 |
| Square root | 120.399336 (= 4√906) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 19 |
| Scientific notation | 1.4496 × |
14496 in other forms
| Form | Value |
|---|---|
| In words | fourteen thousand four hundred and ninety-six |
| Binary (base 2) | 11100010100000 |
| Octal (base 8) | 34240 |
| Hexadecimal (base 16) | 38A0 |
| Base 3 | 201212220 |
| As time | 14496 seconds = 4 h 1 min 36 s |
Is 14496 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (14496 ÷ 2 = 7248) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (14496 ÷ 3 = 4832) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (14496 ÷ 4 = 3624) | 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 (14496 ÷ 6 = 2416) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (14496 ÷ 8 = 1812) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (14496 ÷ 12 = 1208) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 14496 a prime number?
No. 14496 = × 3 × 151, so it is divisible by 2.
What are the factors of 14496?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 151, 302, 453, 604, 906, 1208, 1812, 2416, 3624, 4832, 7248, 14496.
What is 14496 in binary?
11100010100000 (hexadecimal 38A0, octal 34240).
What is the square root of 14496?
About 120.3993, exactly 4√906.
Is 14496 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 14496?
14496 is a Harshad number: divisible by its digit sum 24.