The number 53880
53880 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 449. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 53880.
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How to work it out
- 1
What is special about 53880: a Harshad number: divisible by its digit sum 24.
- 2
53880 is composite. Its prime factorisation is
- 3
The divisors add up to 162000; without 53880 itself that is 108120, so 53880 is abundant (108120 is more than 53880). Euler's totient φ(53880) = 14336 numbers up to 53880 share no factor with it.
- 4
The digits of 53880 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 91 steps to reach 1.
LaTeX source of the formulas on this page
\[ 53880 = 2^{3} \times 3 \times 5 \times 449 \]53880 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 162000 |
| Euler totient φ(n) | 14336 |
| Square | 2903054400 |
| Cube | 156416571072000 |
| Square root | 232.120658 (= 2√13470) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 91 |
| Scientific notation | 5.388 × |
53880 in other forms
| Form | Value |
|---|---|
| In words | fifty-three thousand eight hundred and eighty |
| Binary (base 2) | 1101001001111000 |
| Octal (base 8) | 151170 |
| Hexadecimal (base 16) | D278 |
| Base 3 | 2201220120 |
| As time | 53880 seconds = 14 h 58 min 0 s |
Is 53880 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (53880 ÷ 2 = 26940) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (53880 ÷ 3 = 17960) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (53880 ÷ 4 = 13470) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (53880 ÷ 5 = 10776) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (53880 ÷ 6 = 8980) | 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 (53880 ÷ 8 = 6735) | 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 (53880 ÷ 10 = 5388) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (53880 ÷ 12 = 4490) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 53880 a prime number?
No. 53880 = × 3 × 5 × 449, so it is divisible by 2.
What are the factors of 53880?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 449, 898, 1347, 1796, 2245, 2694, 3592, 4490, 5388, 6735, 8980, 10776, 13470, 17960, 26940, 53880.
What is 53880 in binary?
1101001001111000 (hexadecimal D278, octal 151170).
What is the square root of 53880?
About 232.1207, exactly 2√13470.
Is 53880 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 53880?
53880 is a Harshad number: divisible by its digit sum 24.