The number 77004
77004 is a composite number with 48 divisors. Its prime factorisation is × × 23 × 31. Divisors (48): 1, 2, 3, 4, 6, 9, 12, 18, 23, 27, 31, 36, 46, 54, 62, 69 … 77004.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77004: a Harshad number: divisible by its digit sum 18.
- 2
77004 is composite. Its prime factorisation is
- 3
The divisors add up to 215040; without 77004 itself that is 138036, so 77004 is abundant (138036 is more than 77004). Euler's totient φ(77004) = 23760 numbers up to 77004 share no factor with it.
- 4
The digits of 77004 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77004 = 2^{2} \times 3^{3} \times 23 \times 31 \]77004 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 215040 |
| Euler totient φ(n) | 23760 |
| Square | 5929616016 |
| Cube | 456604151696064 |
| Square root | 277.495946 (= 6√2139) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.7004 × |
77004 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand and four |
| Binary (base 2) | 10010110011001100 |
| Octal (base 8) | 226314 |
| Hexadecimal (base 16) | 12CCC |
| Base 3 | 10220122000 |
| As time | 77004 seconds = 21 h 23 min 24 s |
Is 77004 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77004 ÷ 2 = 38502) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77004 ÷ 3 = 25668) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77004 ÷ 4 = 19251) | 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 (77004 ÷ 6 = 12834) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (77004 ÷ 9 = 8556) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77004 ÷ 12 = 6417) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77004 a prime number?
No. 77004 = × × 23 × 31, so it is divisible by 2.
What are the factors of 77004?
1, 2, 3, 4, 6, 9, 12, 18, 23, 27, 31, 36, 46, 54, 62, 69, 92, 93, 108, 124, 138, 186, 207, 276, 279, 372, 414, 558, 621, 713, 828, 837, 1116, 1242, 1426, 1674, 2139, 2484, 2852, 3348, 4278, 6417, 8556, 12834, 19251, 25668, 38502, 77004.
What is 77004 in binary?
10010110011001100 (hexadecimal 12CCC, octal 226314).
What is the square root of 77004?
About 277.4959, exactly 6√2139.
Is 77004 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 77004?
77004 is a Harshad number: divisible by its digit sum 18.