The number 3301
3301 is a twin prime (3299 and 3301 are both prime) and the 464th prime number. Its only divisors are 1 and 3301.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 3301: a twin prime (3299 and 3301 are both prime); the 464th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
3301 is prime, so its only factors are 1 and 3301. It is the 464th prime; the next prime is 3307 and the one before is 3299.
- 3
The divisors add up to 3302; without 3301 itself that is 1, so 3301 is deficient (1 is less than 3301). Euler's totient φ(3301) = 3300 numbers up to 3301 share no factor with it.
- 4
The digits of 3301 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 136 steps to reach 1.
3301 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 3302 |
| Euler totient φ(n) | 3300 |
| Square | 10896601 |
| Cube | 35969679901 |
| Square root | 57.454330 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 136 |
| Scientific notation | 3.301 × |
3301 in other forms
| Form | Value |
|---|---|
| In words | three thousand three hundred and one |
| Roman numerals | MMMCCCI |
| Binary (base 2) | 110011100101 |
| Octal (base 8) | 6345 |
| Hexadecimal (base 16) | CE5 |
| Base 3 | 11112021 |
| As time | 3301 seconds = 55 min 1 s |
Is 3301 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 1) | 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 1) | 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 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3301 a prime number?
Yes. 3301 is divisible only by 1 and itself.
What are the factors of 3301?
1, 3301.
What is 3301 in binary?
110011100101 (hexadecimal CE5, octal 6345).
What is the square root of 3301?
About 57.4543.
What is 3301 in Roman numerals?
MMMCCCI.
Is 3301 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 3301?
3301 is a twin prime (3299 and 3301 are both prime); the 464th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.