The number 84480
84480 is a composite number with 80 divisors. Its prime factorisation is × 3 × 5 × 11. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30 … 84480.
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How to work it out
- 1
What is special about 84480: a Harshad number: divisible by its digit sum 24.
- 2
84480 is composite. Its prime factorisation is
- 3
The divisors add up to 294624; without 84480 itself that is 210144, so 84480 is abundant (210144 is more than 84480). Euler's totient φ(84480) = 20480 numbers up to 84480 share no factor with it.
- 4
The digits of 84480 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 120 steps to reach 1.
LaTeX source of the formulas on this page
\[ 84480 = 2^{9} \times 3 \times 5 \times 11 \]84480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 294624 |
| Euler totient φ(n) | 20480 |
| Square | 7136870400 |
| Cube | 602922811392000 |
| Square root | 290.654434 (= 16√330) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 120 |
| Scientific notation | 8.448 × |
84480 in other forms
| Form | Value |
|---|---|
| In words | eighty-four thousand four hundred and eighty |
| Binary (base 2) | 10100101000000000 |
| Octal (base 8) | 245000 |
| Hexadecimal (base 16) | 14A00 |
| Base 3 | 11021212220 |
| As time | 84480 seconds = 23 h 28 min 0 s |
Is 84480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (84480 ÷ 2 = 42240) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (84480 ÷ 3 = 28160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (84480 ÷ 4 = 21120) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (84480 ÷ 5 = 16896) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (84480 ÷ 6 = 14080) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (84480 ÷ 8 = 10560) | 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 | Yes (84480 ÷ 10 = 8448) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (84480 ÷ 11 = 7680) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (84480 ÷ 12 = 7040) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 84480 a prime number?
No. 84480 = × 3 × 5 × 11, so it is divisible by 2.
What are the factors of 84480?
1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 64, 66, 80, 88, 96, 110, 120, 128, 132, 160, 165, 176, 192, 220, 240, 256, 264, 320, 330, 352, 384, 440, 480, 512, 528, 640, 660, 704, 768, 880, 960, 1056, 1280, 1320, 1408, 1536, 1760, 1920, 2112, 2560, 2640, 2816, 3520, 3840, 4224, 5280, 5632, 7040, 7680, 8448, 10560, 14080, 16896, 21120, 28160, 42240, 84480.
What is 84480 in binary?
10100101000000000 (hexadecimal 14A00, octal 245000).
What is the square root of 84480?
About 290.6544, exactly 16√330.
Is 84480 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 84480?
84480 is a Harshad number: divisible by its digit sum 24.