The number 3677
3677 is the 514th prime number. Its only divisors are 1 and 3677.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3677: the 514th prime number.
- 2
3677 is prime, so its only factors are 1 and 3677. It is the 514th prime; the next prime is 3691 and the one before is 3673.
- 3
The divisors add up to 3678; without 3677 itself that is 1, so 3677 is deficient (1 is less than 3677). Euler's totient φ(3677) = 3676 numbers up to 3677 share no factor with it.
- 4
The digits of 3677 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 131 steps to reach 1.
3677 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 3678 |
| Euler totient φ(n) | 3676 |
| Square | 13520329 |
| Cube | 49714249733 |
| Square root | 60.638272 |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 131 |
| Scientific notation | 3.677 × |
3677 in other forms
| Form | Value |
|---|---|
| In words | three thousand six hundred and seventy-seven |
| Roman numerals | MMMDCLXXVII |
| Binary (base 2) | 111001011101 |
| Octal (base 8) | 7135 |
| Hexadecimal (base 16) | E5D |
| Base 3 | 12001012 |
| As time | 3677 seconds = 1 h 1 min 17 s |
Is 3677 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 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 5) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3677 a prime number?
Yes. 3677 is divisible only by 1 and itself.
What are the factors of 3677?
1, 3677.
What is 3677 in binary?
111001011101 (hexadecimal E5D, octal 7135).
What is the square root of 3677?
About 60.6383.
What is 3677 in Roman numerals?
MMMDCLXXVII.
Is 3677 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 3677?
3677 is the 514th prime number.