The number 77028
77028 is a triangular number: 1 + 2 + … + 392 = 77028. Its prime factorisation is × 3 × × 131. Divisors (36): 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 131, 147 … 77028.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77028: a triangular number: 1 + 2 + … + 392 = 77028.
- 2
77028 is composite. Its prime factorisation is
- 3
The divisors add up to 210672; without 77028 itself that is 133644, so 77028 is abundant (133644 is more than 77028). Euler's totient φ(77028) = 21840 numbers up to 77028 share no factor with it.
- 4
The digits of 77028 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 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77028 = 2^{2} \times 3 \times 7^{2} \times 131 \]77028 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 210672 |
| Euler totient φ(n) | 21840 |
| Square | 5933312784 |
| Cube | 457031217125952 |
| Square root | 277.539186 (= 14√393) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 107 |
| Scientific notation | 7.7028 × |
77028 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand and twenty-eight |
| Binary (base 2) | 10010110011100100 |
| Octal (base 8) | 226344 |
| Hexadecimal (base 16) | 12CE4 |
| Base 3 | 10220122220 |
| As time | 77028 seconds = 21 h 23 min 48 s |
Is 77028 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77028 ÷ 2 = 38514) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77028 ÷ 3 = 25676) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77028 ÷ 4 = 19257) | 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 (77028 ÷ 6 = 12838) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (77028 ÷ 7 = 11004) | 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 | No (remainder 6) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77028 ÷ 12 = 6419) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77028 a prime number?
No. 77028 = × 3 × × 131, so it is divisible by 2.
What are the factors of 77028?
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 131, 147, 196, 262, 294, 393, 524, 588, 786, 917, 1572, 1834, 2751, 3668, 5502, 6419, 11004, 12838, 19257, 25676, 38514, 77028.
What is 77028 in binary?
10010110011100100 (hexadecimal 12CE4, octal 226344).
What is the square root of 77028?
About 277.5392, exactly 14√393.
Is 77028 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 77028?
77028 is a triangular number: 1 + 2 + … + 392 = 77028.