The number 413
413 is a composite number with 4 divisors. Its prime factorisation is 7 × 59. Divisors (4): 1, 7, 59, 413.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 413: a semiprime: 7 × 59, the product of two primes.
- 2
413 is composite. Its prime factorisation is
- 3
The divisors add up to 480; without 413 itself that is 67, so 413 is deficient (67 is less than 413). Euler's totient φ(413) = 348 numbers up to 413 share no factor with it.
- 4
The digits of 413 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 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 413 = 7 \times 59 \]
413 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 480 |
| Euler totient φ(n) | 348 |
| Square | 170569 |
| Cube | 70444997 |
| Square root | 20.322401 |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 89 |
| Scientific notation | 4.13 × |
413 in other forms
| Form | Value |
|---|---|
| In words | four hundred and thirteen |
| Roman numerals | CDXIII |
| Binary (base 2) | 110011101 |
| Octal (base 8) | 635 |
| Hexadecimal (base 16) | 19D |
| Base 3 | 120022 |
| As time | 413 seconds = 6 min 53 s |
Is 413 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 3) | 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 | Yes (413 ÷ 7 = 59) | 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 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | 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 413 a prime number?
No. 413 = 7 × 59, so it is divisible by 7.
What are the factors of 413?
1, 7, 59, 413.
What is 413 in binary?
110011101 (hexadecimal 19D, octal 635).
What is the square root of 413?
About 20.3224.
What is 413 in Roman numerals?
CDXIII.
Is 413 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 413?
413 is a semiprime: 7 × 59, the product of two primes.