The number 77064
77064 is a composite number with 48 divisors. Its prime factorisation is × 3 × × 19. Divisors (48): 1, 2, 3, 4, 6, 8, 12, 13, 19, 24, 26, 38, 39, 52, 57, 76 … 77064.
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How to work it out
- 1
What is special about 77064: a Harshad number: divisible by its digit sum 24.
- 2
77064 is composite. Its prime factorisation is
- 3
The divisors add up to 219600; without 77064 itself that is 142536, so 77064 is abundant (142536 is more than 77064). Euler's totient φ(77064) = 22464 numbers up to 77064 share no factor with it.
- 4
The digits of 77064 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 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77064 = 2^{3} \times 3 \times 13^{2} \times 19 \]77064 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 219600 |
| Euler totient φ(n) | 22464 |
| Square | 5938860096 |
| Cube | 457672314438144 |
| Square root | 277.604035 (= 26√114) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.7064 × |
77064 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand and sixty-four |
| Binary (base 2) | 10010110100001000 |
| Octal (base 8) | 226410 |
| Hexadecimal (base 16) | 12D08 |
| Base 3 | 10220201020 |
| As time | 77064 seconds = 21 h 24 min 24 s |
Is 77064 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77064 ÷ 2 = 38532) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77064 ÷ 3 = 25688) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77064 ÷ 4 = 19266) | 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 (77064 ÷ 6 = 12844) | 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 (77064 ÷ 8 = 9633) | 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 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 | Yes (77064 ÷ 12 = 6422) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77064 a prime number?
No. 77064 = × 3 × × 19, so it is divisible by 2.
What are the factors of 77064?
1, 2, 3, 4, 6, 8, 12, 13, 19, 24, 26, 38, 39, 52, 57, 76, 78, 104, 114, 152, 156, 169, 228, 247, 312, 338, 456, 494, 507, 676, 741, 988, 1014, 1352, 1482, 1976, 2028, 2964, 3211, 4056, 5928, 6422, 9633, 12844, 19266, 25688, 38532, 77064.
What is 77064 in binary?
10010110100001000 (hexadecimal 12D08, octal 226410).
What is the square root of 77064?
About 277.6040, exactly 26√114.
Is 77064 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 77064?
77064 is a Harshad number: divisible by its digit sum 24.