The number 1607
1607 is a twin prime (1607 and 1609 are both prime) and the 253rd prime number. Its only divisors are 1 and 1607.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1607: a twin prime (1607 and 1609 are both prime); the 253rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1607 is prime, so its only factors are 1 and 1607. It is the 253rd prime; the next prime is 1609 and the one before is 1601.
- 3
The divisors add up to 1608; without 1607 itself that is 1, so 1607 is deficient (1 is less than 1607). Euler's totient φ(1607) = 1606 numbers up to 1607 share no factor with it.
- 4
The digits of 1607 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 166 steps to reach 1.
1607 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1608 |
| Euler totient φ(n) | 1606 |
| Square | 2582449 |
| Cube | 4149995543 |
| Square root | 40.087405 |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 166 |
| Scientific notation | 1.607 × |
1607 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and seven |
| Roman numerals | MDCVII |
| Binary (base 2) | 11001000111 |
| Octal (base 8) | 3107 |
| Hexadecimal (base 16) | 647 |
| Base 3 | 2012112 |
| As time | 1607 seconds = 26 min 47 s |
Is 1607 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 4) | 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 7) | 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 1) | 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 1607 a prime number?
Yes. 1607 is divisible only by 1 and itself.
What are the factors of 1607?
1, 1607.
What is 1607 in binary?
11001000111 (hexadecimal 647, octal 3107).
What is the square root of 1607?
About 40.0874.
What is 1607 in Roman numerals?
MDCVII.
Is 1607 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 1607?
1607 is a twin prime (1607 and 1609 are both prime); the 253rd prime number; a happy number: repeatedly adding the squares of its digits reaches 1.