The number 1667
1667 is a twin prime (1667 and 1669 are both prime) and the 262nd prime number. Its only divisors are 1 and 1667.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1667: a twin prime (1667 and 1669 are both prime); the 262nd prime number.
- 2
1667 is prime, so its only factors are 1 and 1667. It is the 262nd prime; the next prime is 1669 and the one before is 1663.
- 3
The divisors add up to 1668; without 1667 itself that is 1, so 1667 is deficient (1 is less than 1667). Euler's totient φ(1667) = 1666 numbers up to 1667 share no factor with it.
- 4
The digits of 1667 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
1667 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1668 |
| Euler totient φ(n) | 1666 |
| Square | 2778889 |
| Cube | 4632407963 |
| Square root | 40.828911 |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.667 × |
1667 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and sixty-seven |
| Roman numerals | MDCLXVII |
| Binary (base 2) | 11010000011 |
| Octal (base 8) | 3203 |
| Hexadecimal (base 16) | 683 |
| Base 3 | 2021202 |
| As time | 1667 seconds = 27 min 47 s |
Is 1667 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 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 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 6) | 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 1667 a prime number?
Yes. 1667 is divisible only by 1 and itself.
What are the factors of 1667?
1, 1667.
What is 1667 in binary?
11010000011 (hexadecimal 683, octal 3203).
What is the square root of 1667?
About 40.8289.
What is 1667 in Roman numerals?
MDCLXVII.
Is 1667 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 1667?
1667 is a twin prime (1667 and 1669 are both prime); the 262nd prime number.