The number 55440
55440 is a highly composite number: it has 120 divisors, more than any smaller number. Its prime factorisation is × × 5 × 7 × 11. Divisors (120): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18 … 55440.
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How to work it out
- 1
What is special about 55440: a highly composite number: it has 120 divisors, more than any smaller number; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
55440 is composite. Its prime factorisation is
- 3
The divisors add up to 232128; without 55440 itself that is 176688, so 55440 is abundant (176688 is more than 55440). Euler's totient φ(55440) = 11520 numbers up to 55440 share no factor with it.
- 4
The digits of 55440 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 153 steps to reach 1.
LaTeX source of the formulas on this page
\[ 55440 = 2^{4} \times 3^{2} \times 5 \times 7 \times 11 \]55440 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 120 |
| Sum of divisors | 232128 |
| Euler totient φ(n) | 11520 |
| Square | 3073593600 |
| Cube | 170400029184000 |
| Square root | 235.457002 (= 12√385) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 153 |
| Scientific notation | 5.544 × |
55440 in other forms
| Form | Value |
|---|---|
| In words | fifty-five thousand four hundred and forty |
| Binary (base 2) | 1101100010010000 |
| Octal (base 8) | 154220 |
| Hexadecimal (base 16) | D890 |
| Base 3 | 2211001100 |
| As time | 55440 seconds = 15 h 24 min 0 s |
Is 55440 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (55440 ÷ 2 = 27720) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (55440 ÷ 3 = 18480) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (55440 ÷ 4 = 13860) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (55440 ÷ 5 = 11088) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (55440 ÷ 6 = 9240) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (55440 ÷ 7 = 7920) | 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 (55440 ÷ 8 = 6930) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (55440 ÷ 9 = 6160) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (55440 ÷ 10 = 5544) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (55440 ÷ 11 = 5040) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (55440 ÷ 12 = 4620) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 55440 a prime number?
No. 55440 = × × 5 × 7 × 11, so it is divisible by 2.
What are the factors of 55440?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 28, 30, 33, 35, 36, 40, 42, 44, 45, 48, 55, 56, 60, 63, 66, 70, 72, 77, 80, 84, 88, 90, 99, 105, 110, 112, 120, 126, 132, 140, 144, 154, 165, 168, 176, 180, 198, 210, 220, 231, 240, 252, 264, 280, 308, 315, 330, 336, 360, 385, 396, 420, 440, 462, 495, 504, 528, 560, 616, 630, 660, 693, 720, 770, 792, 840, 880, 924, 990, 1008, 1155, 1232, 1260, 1320, 1386, 1540, 1584, 1680, 1848, 1980, 2310, 2520, 2640, 2772, 3080, 3465, 3696, 3960, 4620, 5040, 5544, 6160, 6930, 7920, 9240, 11088, 13860, 18480, 27720, 55440.
What is 55440 in binary?
1101100010010000 (hexadecimal D890, octal 154220).
What is the square root of 55440?
About 235.4570, exactly 12√385.
Is 55440 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 55440?
55440 is a highly composite number: it has 120 divisors, more than any smaller number; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.