The number 2801
2801 is a twin prime (2801 and 2803 are both prime) and the 408th prime number. Its only divisors are 1 and 2801.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2801: a twin prime (2801 and 2803 are both prime); the 408th prime number.
- 2
2801 is prime, so its only factors are 1 and 2801. It is the 408th prime; the next prime is 2803 and the one before is 2797.
- 3
The divisors add up to 2802; without 2801 itself that is 1, so 2801 is deficient (1 is less than 2801). Euler's totient φ(2801) = 2800 numbers up to 2801 share no factor with it.
- 4
The digits of 2801 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 35 steps to reach 1.
2801 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 2802 |
| Euler totient φ(n) | 2800 |
| Square | 7845601 |
| Cube | 21975528401 |
| Square root | 52.924474 |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 35 |
| Scientific notation | 2.801 × |
2801 in other forms
| Form | Value |
|---|---|
| In words | two thousand eight hundred and one |
| Roman numerals | MMDCCCI |
| Binary (base 2) | 101011110001 |
| Octal (base 8) | 5361 |
| Hexadecimal (base 16) | AF1 |
| Base 3 | 10211202 |
| As time | 2801 seconds = 46 min 41 s |
Is 2801 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 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 2) | 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 7) | 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 2801 a prime number?
Yes. 2801 is divisible only by 1 and itself.
What are the factors of 2801?
1, 2801.
What is 2801 in binary?
101011110001 (hexadecimal AF1, octal 5361).
What is the square root of 2801?
About 52.9245.
What is 2801 in Roman numerals?
MMDCCCI.
Is 2801 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 2801?
2801 is a twin prime (2801 and 2803 are both prime); the 408th prime number.