The number 78480
78480 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 109. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 78480.
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How to work it out
- 1
What is special about 78480: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
78480 is composite. Its prime factorisation is
- 3
The divisors add up to 265980; without 78480 itself that is 187500, so 78480 is abundant (187500 is more than 78480). Euler's totient φ(78480) = 20736 numbers up to 78480 share no factor with it.
- 4
The digits of 78480 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 169 steps to reach 1.
LaTeX source of the formulas on this page
\[ 78480 = 2^{4} \times 3^{2} \times 5 \times 109 \]78480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 265980 |
| Euler totient φ(n) | 20736 |
| Square | 6159110400 |
| Cube | 483366984192000 |
| Square root | 280.142821 (= 12√545) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 169 |
| Scientific notation | 7.848 × |
78480 in other forms
| Form | Value |
|---|---|
| In words | seventy-eight thousand four hundred and eighty |
| Binary (base 2) | 10011001010010000 |
| Octal (base 8) | 231220 |
| Hexadecimal (base 16) | 13290 |
| Base 3 | 10222122200 |
| As time | 78480 seconds = 21 h 48 min 0 s |
Is 78480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (78480 ÷ 2 = 39240) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (78480 ÷ 3 = 26160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (78480 ÷ 4 = 19620) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (78480 ÷ 5 = 15696) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (78480 ÷ 6 = 13080) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (78480 ÷ 8 = 9810) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (78480 ÷ 9 = 8720) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (78480 ÷ 10 = 7848) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (78480 ÷ 12 = 6540) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 78480 a prime number?
No. 78480 = × × 5 × 109, so it is divisible by 2.
What are the factors of 78480?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 109, 120, 144, 180, 218, 240, 327, 360, 436, 545, 654, 720, 872, 981, 1090, 1308, 1635, 1744, 1962, 2180, 2616, 3270, 3924, 4360, 4905, 5232, 6540, 7848, 8720, 9810, 13080, 15696, 19620, 26160, 39240, 78480.
What is 78480 in binary?
10011001010010000 (hexadecimal 13290, octal 231220).
What is the square root of 78480?
About 280.1428, exactly 12√545.
Is 78480 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 78480?
78480 is a happy number: repeatedly adding the squares of its digits reaches 1.