The number 78072
78072 is a composite number with 16 divisors. Its prime factorisation is × 3 × 3253. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 3253, 6506, 9759, 13012, 19518, 26024, 39036, 78072.
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How to work it out
- 1
What is special about 78072: a Harshad number: divisible by its digit sum 24.
- 2
78072 is composite. Its prime factorisation is
- 3
The divisors add up to 195240; without 78072 itself that is 117168, so 78072 is abundant (117168 is more than 78072). Euler's totient φ(78072) = 26016 numbers up to 78072 share no factor with it.
- 4
The digits of 78072 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 156 steps to reach 1.
LaTeX source of the formulas on this page
\[ 78072 = 2^{3} \times 3 \times 3253 \]78072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 195240 |
| Euler totient φ(n) | 26016 |
| Square | 6095237184 |
| Cube | 475867357429248 |
| Square root | 279.413672 (= 2√19518) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 156 |
| Scientific notation | 7.8072 × |
78072 in other forms
| Form | Value |
|---|---|
| In words | seventy-eight thousand and seventy-two |
| Binary (base 2) | 10011000011111000 |
| Octal (base 8) | 230370 |
| Hexadecimal (base 16) | 130F8 |
| Base 3 | 10222002120 |
| As time | 78072 seconds = 21 h 41 min 12 s |
Is 78072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (78072 ÷ 2 = 39036) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (78072 ÷ 3 = 26024) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (78072 ÷ 4 = 19518) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (78072 ÷ 6 = 13012) | 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 (78072 ÷ 8 = 9759) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (78072 ÷ 12 = 6506) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 78072 a prime number?
No. 78072 = × 3 × 3253, so it is divisible by 2.
What are the factors of 78072?
1, 2, 3, 4, 6, 8, 12, 24, 3253, 6506, 9759, 13012, 19518, 26024, 39036, 78072.
What is 78072 in binary?
10011000011111000 (hexadecimal 130F8, octal 230370).
What is the square root of 78072?
About 279.4137, exactly 2√19518.
Is 78072 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 78072?
78072 is a Harshad number: divisible by its digit sum 24.