The number 401
401 is the 79th prime number. Its only divisors are 1 and 401.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 401: the 79th prime number.
- 2
401 is prime, so its only factors are 1 and 401. It is the 79th prime; the next prime is 409 and the one before is 397.
- 3
The divisors add up to 402; without 401 itself that is 1, so 401 is deficient (1 is less than 401). Euler's totient φ(401) = 400 numbers up to 401 share no factor with it.
- 4
The digits of 401 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 19 steps to reach 1.
401 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 402 |
| Euler totient φ(n) | 400 |
| Square | 160801 |
| Cube | 64481201 |
| Square root | 20.024984 |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 19 |
| Scientific notation | 4.01 × |
401 in other forms
| Form | Value |
|---|---|
| In words | four hundred and one |
| Roman numerals | CDI |
| Binary (base 2) | 110010001 |
| Octal (base 8) | 621 |
| Hexadecimal (base 16) | 191 |
| Base 3 | 112212 |
| As time | 401 seconds = 6 min 41 s |
Is 401 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 2) | 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 5) | 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 5) | 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 401 a prime number?
Yes. 401 is divisible only by 1 and itself.
What are the factors of 401?
1, 401.
What is 401 in binary?
110010001 (hexadecimal 191, octal 621).
What is the square root of 401?
About 20.0250.
What is 401 in Roman numerals?
CDI.
Is 401 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 401?
401 is the 79th prime number.