The number 78048
78048 is a composite number with 36 divisors. Its prime factorisation is × × 271. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96 … 78048.
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How to work it out
- 1
What is special about 78048: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
78048 is composite. Its prime factorisation is
- 3
The divisors add up to 222768; without 78048 itself that is 144720, so 78048 is abundant (144720 is more than 78048). Euler's totient φ(78048) = 25920 numbers up to 78048 share no factor with it.
- 4
The digits of 78048 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 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 78048 = 2^{5} \times 3^{2} \times 271 \]78048 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 222768 |
| Euler totient φ(n) | 25920 |
| Square | 6091490304 |
| Cube | 475428635246592 |
| Square root | 279.370721 (= 12√542) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 138 |
| Scientific notation | 7.8048 × |
78048 in other forms
| Form | Value |
|---|---|
| In words | seventy-eight thousand and forty-eight |
| Binary (base 2) | 10011000011100000 |
| Octal (base 8) | 230340 |
| Hexadecimal (base 16) | 130E0 |
| Base 3 | 10222001200 |
| As time | 78048 seconds = 21 h 40 min 48 s |
Is 78048 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (78048 ÷ 2 = 39024) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (78048 ÷ 3 = 26016) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (78048 ÷ 4 = 19512) | 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 (78048 ÷ 6 = 13008) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (78048 ÷ 8 = 9756) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (78048 ÷ 9 = 8672) | 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 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (78048 ÷ 12 = 6504) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 78048 a prime number?
No. 78048 = × × 271, so it is divisible by 2.
What are the factors of 78048?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 271, 288, 542, 813, 1084, 1626, 2168, 2439, 3252, 4336, 4878, 6504, 8672, 9756, 13008, 19512, 26016, 39024, 78048.
What is 78048 in binary?
10011000011100000 (hexadecimal 130E0, octal 230340).
What is the square root of 78048?
About 279.3707, exactly 12√542.
Is 78048 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 78048?
78048 is a happy number: repeatedly adding the squares of its digits reaches 1.