The number 87840
87840 is a composite number with 72 divisors. Its prime factorisation is × × 5 × 61. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 87840.
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How to work it out
- 1
What is special about 87840: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
87840 is composite. Its prime factorisation is
- 3
The divisors add up to 304668; without 87840 itself that is 216828, so 87840 is abundant (216828 is more than 87840). Euler's totient φ(87840) = 23040 numbers up to 87840 share no factor with it.
- 4
The digits of 87840 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87840 = 2^{5} \times 3^{2} \times 5 \times 61 \]87840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 304668 |
| Euler totient φ(n) | 23040 |
| Square | 7715865600 |
| Cube | 677761634304000 |
| Square root | 296.378137 (= 12√610) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 45 |
| Scientific notation | 8.784 × |
87840 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand eight hundred and forty |
| Binary (base 2) | 10101011100100000 |
| Octal (base 8) | 253440 |
| Hexadecimal (base 16) | 15720 |
| Base 3 | 11110111100 |
| As time | 87840 seconds = 24 h 24 min 0 s |
Is 87840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87840 ÷ 2 = 43920) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87840 ÷ 3 = 29280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87840 ÷ 4 = 21960) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (87840 ÷ 5 = 17568) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (87840 ÷ 6 = 14640) | 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 (87840 ÷ 8 = 10980) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (87840 ÷ 9 = 9760) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (87840 ÷ 10 = 8784) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (87840 ÷ 12 = 7320) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87840 a prime number?
No. 87840 = × × 5 × 61, so it is divisible by 2.
What are the factors of 87840?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 61, 72, 80, 90, 96, 120, 122, 144, 160, 180, 183, 240, 244, 288, 305, 360, 366, 480, 488, 549, 610, 720, 732, 915, 976, 1098, 1220, 1440, 1464, 1830, 1952, 2196, 2440, 2745, 2928, 3660, 4392, 4880, 5490, 5856, 7320, 8784, 9760, 10980, 14640, 17568, 21960, 29280, 43920, 87840.
What is 87840 in binary?
10101011100100000 (hexadecimal 15720, octal 253440).
What is the square root of 87840?
About 296.3781, exactly 12√610.
Is 87840 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 87840?
87840 is a happy number: repeatedly adding the squares of its digits reaches 1.