The number 17977
17977 is the 2061st prime number. Its only divisors are 1 and 17977.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 17977: the 2061st prime number.
- 2
17977 is prime, so its only factors are 1 and 17977. It is the 2061st prime; the next prime is 17981 and the one before is 17971.
- 3
The divisors add up to 17978; without 17977 itself that is 1, so 17977 is deficient (1 is less than 17977). Euler's totient φ(17977) = 17976 numbers up to 17977 share no factor with it.
- 4
The digits of 17977 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 48 steps to reach 1.
17977 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 17978 |
| Euler totient φ(n) | 17976 |
| Square | 323172529 |
| Cube | 5809672553833 |
| Square root | 134.078335 |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 48 |
| Scientific notation | 1.7977 × |
17977 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand nine hundred and seventy-seven |
| Binary (base 2) | 100011000111001 |
| Octal (base 8) | 43071 |
| Hexadecimal (base 16) | 4639 |
| Base 3 | 220122211 |
| As time | 17977 seconds = 4 h 59 min 37 s |
Is 17977 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 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | 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 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17977 a prime number?
Yes. 17977 is divisible only by 1 and itself.
What are the factors of 17977?
1, 17977.
What is 17977 in binary?
100011000111001 (hexadecimal 4639, octal 43071).
What is the square root of 17977?
About 134.0783.
Is 17977 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 17977?
17977 is the 2061st prime number.