The number 78240
78240 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 163. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 78240.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 78240: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
78240 is composite. Its prime factorisation is
- 3
The divisors add up to 247968; without 78240 itself that is 169728, so 78240 is abundant (169728 is more than 78240). Euler's totient φ(78240) = 20736 numbers up to 78240 share no factor with it.
- 4
The digits of 78240 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 78240 = 2^{5} \times 3 \times 5 \times 163 \]78240 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 247968 |
| Euler totient φ(n) | 20736 |
| Square | 6121497600 |
| Cube | 478945972224000 |
| Square root | 279.714140 (= 4√4890) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 45 |
| Scientific notation | 7.824 × |
78240 in other forms
| Form | Value |
|---|---|
| In words | seventy-eight thousand two hundred and forty |
| Binary (base 2) | 10011000110100000 |
| Octal (base 8) | 230640 |
| Hexadecimal (base 16) | 131A0 |
| Base 3 | 10222022210 |
| As time | 78240 seconds = 21 h 44 min 0 s |
Is 78240 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (78240 ÷ 2 = 39120) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (78240 ÷ 3 = 26080) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (78240 ÷ 4 = 19560) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (78240 ÷ 5 = 15648) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (78240 ÷ 6 = 13040) | 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 (78240 ÷ 8 = 9780) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (78240 ÷ 10 = 7824) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (78240 ÷ 12 = 6520) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 78240 a prime number?
No. 78240 = × 3 × 5 × 163, so it is divisible by 2.
What are the factors of 78240?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 163, 240, 326, 480, 489, 652, 815, 978, 1304, 1630, 1956, 2445, 2608, 3260, 3912, 4890, 5216, 6520, 7824, 9780, 13040, 15648, 19560, 26080, 39120, 78240.
What is 78240 in binary?
10011000110100000 (hexadecimal 131A0, octal 230640).
What is the square root of 78240?
About 279.7141, exactly 4√4890.
Is 78240 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 78240?
78240 is a happy number: repeatedly adding the squares of its digits reaches 1.