The number 78078
78078 is a composite number with 48 divisors. Its prime factorisation is 2 × 3 × 7 × 11 × . Divisors (48): 1, 2, 3, 6, 7, 11, 13, 14, 21, 22, 26, 33, 39, 42, 66, 77 … 78078.
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How to work it out
- 1
What is special about 78078: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
78078 is composite. Its prime factorisation is
- 3
The divisors add up to 210816; without 78078 itself that is 132738, so 78078 is abundant (132738 is more than 78078). Euler's totient φ(78078) = 18720 numbers up to 78078 share no factor with it.
- 4
The digits of 78078 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 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 78078 = 2 \times 3 \times 7 \times 11 \times 13^{2} \]78078 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 210816 |
| Euler totient φ(n) | 18720 |
| Square | 6096174084 |
| Cube | 475977080130552 |
| Square root | 279.424408 (= 13√462) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 63 |
| Scientific notation | 7.8078 × |
78078 in other forms
| Form | Value |
|---|---|
| In words | seventy-eight thousand and seventy-eight |
| Binary (base 2) | 10011000011111110 |
| Octal (base 8) | 230376 |
| Hexadecimal (base 16) | 130FE |
| Base 3 | 10222002210 |
| As time | 78078 seconds = 21 h 41 min 18 s |
Is 78078 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (78078 ÷ 2 = 39039) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (78078 ÷ 3 = 26026) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (78078 ÷ 6 = 13013) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (78078 ÷ 7 = 11154) | 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 6) | 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 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (78078 ÷ 11 = 7098) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 78078 a prime number?
No. 78078 = 2 × 3 × 7 × 11 × , so it is divisible by 2.
What are the factors of 78078?
1, 2, 3, 6, 7, 11, 13, 14, 21, 22, 26, 33, 39, 42, 66, 77, 78, 91, 143, 154, 169, 182, 231, 273, 286, 338, 429, 462, 507, 546, 858, 1001, 1014, 1183, 1859, 2002, 2366, 3003, 3549, 3718, 5577, 6006, 7098, 11154, 13013, 26026, 39039, 78078.
What is 78078 in binary?
10011000011111110 (hexadecimal 130FE, octal 230376).
What is the square root of 78078?
About 279.4244, exactly 13√462.
Is 78078 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 78078?
78078 is a happy number: repeatedly adding the squares of its digits reaches 1.