The number 1601
1601 is the 252nd prime number. Its only divisors are 1 and 1601.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1601: the 252nd prime number.
- 2
1601 is prime, so its only factors are 1 and 1601. It is the 252nd prime; the next prime is 1607 and the one before is 1597.
- 3
The divisors add up to 1602; without 1601 itself that is 1, so 1601 is deficient (1 is less than 1601). Euler's totient φ(1601) = 1600 numbers up to 1601 share no factor with it.
- 4
The digits of 1601 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 60 steps to reach 1.
1601 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1602 |
| Euler totient φ(n) | 1600 |
| Square | 2563201 |
| Cube | 4103684801 |
| Square root | 40.012498 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 60 |
| Scientific notation | 1.601 × |
1601 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and one |
| Roman numerals | MDCI |
| Binary (base 2) | 11001000001 |
| Octal (base 8) | 3101 |
| Hexadecimal (base 16) | 641 |
| Base 3 | 2012022 |
| As time | 1601 seconds = 26 min 41 s |
Is 1601 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 1) | 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 5) | 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 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | 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 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1601 a prime number?
Yes. 1601 is divisible only by 1 and itself.
What are the factors of 1601?
1, 1601.
What is 1601 in binary?
11001000001 (hexadecimal 641, octal 3101).
What is the square root of 1601?
About 40.0125.
What is 1601 in Roman numerals?
MDCI.
Is 1601 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 1601?
1601 is the 252nd prime number.