The number 76734
76734 is a composite number with 48 divisors. Its prime factorisation is 2 × × × 29. Divisors (48): 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 29, 42, 49, 54, 58, 63 … 76734.
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How to work it out
- 1
What is special about 76734: a Harshad number: divisible by its digit sum 27.
- 2
76734 is composite. Its prime factorisation is
- 3
The divisors add up to 205200; without 76734 itself that is 128466, so 76734 is abundant (128466 is more than 76734). Euler's totient φ(76734) = 21168 numbers up to 76734 share no factor with it.
- 4
The digits of 76734 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
\[ 76734 = 2 \times 3^{3} \times 7^{2} \times 29 \]76734 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 205200 |
| Euler totient φ(n) | 21168 |
| Square | 5888106756 |
| Cube | 451817983814904 |
| Square root | 277.009025 (= 21√174) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 138 |
| Scientific notation | 7.6734 × |
76734 in other forms
| Form | Value |
|---|---|
| In words | seventy-six thousand seven hundred and thirty-four |
| Binary (base 2) | 10010101110111110 |
| Octal (base 8) | 225676 |
| Hexadecimal (base 16) | 12BBE |
| Base 3 | 10220021000 |
| As time | 76734 seconds = 21 h 18 min 54 s |
Is 76734 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (76734 ÷ 2 = 38367) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (76734 ÷ 3 = 25578) | 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 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (76734 ÷ 6 = 12789) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (76734 ÷ 7 = 10962) | 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 | Yes (76734 ÷ 9 = 8526) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 76734 a prime number?
No. 76734 = 2 × × × 29, so it is divisible by 2.
What are the factors of 76734?
1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 29, 42, 49, 54, 58, 63, 87, 98, 126, 147, 174, 189, 203, 261, 294, 378, 406, 441, 522, 609, 783, 882, 1218, 1323, 1421, 1566, 1827, 2646, 2842, 3654, 4263, 5481, 8526, 10962, 12789, 25578, 38367, 76734.
What is 76734 in binary?
10010101110111110 (hexadecimal 12BBE, octal 225676).
What is the square root of 76734?
About 277.0090, exactly 21√174.
Is 76734 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 76734?
76734 is a Harshad number: divisible by its digit sum 27.