The number 421
421 is a twin prime (419 and 421 are both prime) and the 82nd prime number. Its only divisors are 1 and 421.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 421: a twin prime (419 and 421 are both prime); the 82nd prime number.
- 2
421 is prime, so its only factors are 1 and 421. It is the 82nd prime; the next prime is 431 and the one before is 419.
- 3
The divisors add up to 422; without 421 itself that is 1, so 421 is deficient (1 is less than 421). Euler's totient φ(421) = 420 numbers up to 421 share no factor with it.
- 4
The digits of 421 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 40 steps to reach 1.
421 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 422 |
| Euler totient φ(n) | 420 |
| Square | 177241 |
| Cube | 74618461 |
| Square root | 20.518285 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 40 |
| Scientific notation | 4.21 × |
421 in other forms
| Form | Value |
|---|---|
| In words | four hundred and twenty-one |
| Roman numerals | CDXXI |
| Binary (base 2) | 110100101 |
| Octal (base 8) | 645 |
| Hexadecimal (base 16) | 1A5 |
| Base 3 | 120121 |
| As time | 421 seconds = 7 min 1 s |
Is 421 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 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 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 3) | 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 421 a prime number?
Yes. 421 is divisible only by 1 and itself.
What are the factors of 421?
1, 421.
What is 421 in binary?
110100101 (hexadecimal 1A5, octal 645).
What is the square root of 421?
About 20.5183.
What is 421 in Roman numerals?
CDXXI.
Is 421 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 421?
421 is a twin prime (419 and 421 are both prime); the 82nd prime number.