The number 10413
10413 is a composite number with 12 divisors. Its prime factorisation is × 13 × 89. Divisors (12): 1, 3, 9, 13, 39, 89, 117, 267, 801, 1157, 3471, 10413.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10413: a Harshad number: divisible by its digit sum 9.
- 2
10413 is composite. Its prime factorisation is
- 3
The divisors add up to 16380; without 10413 itself that is 5967, so 10413 is deficient (5967 is less than 10413). Euler's totient φ(10413) = 6336 numbers up to 10413 share no factor with it.
- 4
The digits of 10413 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 104 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10413 = 3^{2} \times 13 \times 89 \]10413 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 16380 |
| Euler totient φ(n) | 6336 |
| Square | 108430569 |
| Cube | 1129087514997 |
| Square root | 102.044108 (= 3√1157) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 104 |
| Scientific notation | 1.0413 × |
10413 in other forms
| Form | Value |
|---|---|
| In words | ten thousand four hundred and thirteen |
| Binary (base 2) | 10100010101101 |
| Octal (base 8) | 24255 |
| Hexadecimal (base 16) | 28AD |
| Base 3 | 112021200 |
| As time | 10413 seconds = 2 h 53 min 33 s |
Is 10413 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 | Yes (10413 ÷ 3 = 3471) | 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 3) | 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 | Yes (10413 ÷ 9 = 1157) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10413 a prime number?
No. 10413 = × 13 × 89, so it is divisible by 3.
What are the factors of 10413?
1, 3, 9, 13, 39, 89, 117, 267, 801, 1157, 3471, 10413.
What is 10413 in binary?
10100010101101 (hexadecimal 28AD, octal 24255).
What is the square root of 10413?
About 102.0441, exactly 3√1157.
Is 10413 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 10413?
10413 is a Harshad number: divisible by its digit sum 9.