The number 77003
77003 is the 7568th prime number. Its only divisors are 1 and 77003.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77003: the 7568th prime number.
- 2
77003 is prime, so its only factors are 1 and 77003. It is the 7568th prime; the next prime is 77017 and the one before is 76991.
- 3
The divisors add up to 77004; without 77003 itself that is 1, so 77003 is deficient (1 is less than 77003). Euler's totient φ(77003) = 77002 numbers up to 77003 share no factor with it.
- 4
The digits of 77003 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
77003 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 77004 |
| Euler totient φ(n) | 77002 |
| Square | 5929462009 |
| Cube | 456586363079027 |
| Square root | 277.494144 |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.7003 × |
77003 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand and three |
| Binary (base 2) | 10010110011001011 |
| Octal (base 8) | 226313 |
| Hexadecimal (base 16) | 12CCB |
| Base 3 | 10220121222 |
| As time | 77003 seconds = 21 h 23 min 23 s |
Is 77003 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | 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 | No (remainder 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77003 a prime number?
Yes. 77003 is divisible only by 1 and itself.
What are the factors of 77003?
1, 77003.
What is 77003 in binary?
10010110011001011 (hexadecimal 12CCB, octal 226313).
What is the square root of 77003?
About 277.4941.
Is 77003 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 77003?
77003 is the 7568th prime number.