The number 78780
78780 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 13 × 101. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60 … 78780.
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How to work it out
- 1
What is special about 78780: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.
- 2
78780 is composite. Its prime factorisation is
- 3
The divisors add up to 239904; without 78780 itself that is 161124, so 78780 is abundant (161124 is more than 78780). Euler's totient φ(78780) = 19200 numbers up to 78780 share no factor with it.
- 4
The digits of 78780 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 78780 = 2^{2} \times 3 \times 5 \times 13 \times 101 \]78780 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 239904 |
| Euler totient φ(n) | 19200 |
| Square | 6206288400 |
| Cube | 488931400152000 |
| Square root | 280.677751 (= 2√19695) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 107 |
| Scientific notation | 7.878 × |
78780 in other forms
| Form | Value |
|---|---|
| In words | seventy-eight thousand seven hundred and eighty |
| Binary (base 2) | 10011001110111100 |
| Octal (base 8) | 231674 |
| Hexadecimal (base 16) | 133BC |
| Base 3 | 11000001210 |
| As time | 78780 seconds = 21 h 53 min 0 s |
Is 78780 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (78780 ÷ 2 = 39390) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (78780 ÷ 3 = 26260) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (78780 ÷ 4 = 19695) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (78780 ÷ 5 = 15756) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (78780 ÷ 6 = 13130) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | No (remainder 4) | 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 (78780 ÷ 10 = 7878) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (78780 ÷ 12 = 6565) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 78780 a prime number?
No. 78780 = × 3 × 5 × 13 × 101, so it is divisible by 2.
What are the factors of 78780?
1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 101, 130, 156, 195, 202, 260, 303, 390, 404, 505, 606, 780, 1010, 1212, 1313, 1515, 2020, 2626, 3030, 3939, 5252, 6060, 6565, 7878, 13130, 15756, 19695, 26260, 39390, 78780.
What is 78780 in binary?
10011001110111100 (hexadecimal 133BC, octal 231674).
What is the square root of 78780?
About 280.6778, exactly 2√19695.
Is 78780 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 78780?
78780 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 30.