The number 77100
77100 is a composite number with 36 divisors. Its prime factorisation is × 3 × × 257. Divisors (36): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100 … 77100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77100: a Harshad number: divisible by its digit sum 15.
- 2
77100 is composite. Its prime factorisation is
- 3
The divisors add up to 223944; without 77100 itself that is 146844, so 77100 is abundant (146844 is more than 77100). Euler's totient φ(77100) = 20480 numbers up to 77100 share no factor with it.
- 4
The digits of 77100 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77100 = 2^{2} \times 3 \times 5^{2} \times 257 \]77100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 223944 |
| Euler totient φ(n) | 20480 |
| Square | 5944410000 |
| Cube | 458314011000000 |
| Square root | 277.668868 (= 10√771) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.71 × |
77100 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand one hundred |
| Binary (base 2) | 10010110100101100 |
| Octal (base 8) | 226454 |
| Hexadecimal (base 16) | 12D2C |
| Base 3 | 10220202120 |
| As time | 77100 seconds = 21 h 25 min 0 s |
Is 77100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77100 ÷ 2 = 38550) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77100 ÷ 3 = 25700) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77100 ÷ 4 = 19275) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77100 ÷ 5 = 15420) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77100 ÷ 6 = 12850) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (77100 ÷ 10 = 7710) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77100 ÷ 12 = 6425) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77100 a prime number?
No. 77100 = × 3 × × 257, so it is divisible by 2.
What are the factors of 77100?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 257, 300, 514, 771, 1028, 1285, 1542, 2570, 3084, 3855, 5140, 6425, 7710, 12850, 15420, 19275, 25700, 38550, 77100.
What is 77100 in binary?
10010110100101100 (hexadecimal 12D2C, octal 226454).
What is the square root of 77100?
About 277.6689, exactly 10√771.
Is 77100 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 77100?
77100 is a Harshad number: divisible by its digit sum 15.