The number 90013
90013 is a composite number with 12 divisors. Its prime factorisation is × 11 × 167. Divisors (12): 1, 7, 11, 49, 77, 167, 539, 1169, 1837, 8183, 12859, 90013.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90013: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
90013 is composite. Its prime factorisation is
- 3
The divisors add up to 114912; without 90013 itself that is 24899, so 90013 is deficient (24899 is less than 90013). Euler's totient φ(90013) = 69720 numbers up to 90013 share no factor with it.
- 4
The digits of 90013 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 164 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90013 = 7^{2} \times 11 \times 167 \]90013 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 114912 |
| Euler totient φ(n) | 69720 |
| Square | 8102340169 |
| Cube | 729315945632197 |
| Square root | 300.021666 (= 7√1837) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 164 |
| Scientific notation | 9.0013 × |
90013 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand and thirteen |
| Binary (base 2) | 10101111110011101 |
| Octal (base 8) | 257635 |
| Hexadecimal (base 16) | 15F9D |
| Base 3 | 11120110211 |
| As time | 90013 seconds = 25 h 0 min 13 s |
Is 90013 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 3) | 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 | Yes (90013 ÷ 7 = 12859) | 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 4) | 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 | Yes (90013 ÷ 11 = 8183) | 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 90013 a prime number?
No. 90013 = × 11 × 167, so it is divisible by 7.
What are the factors of 90013?
1, 7, 11, 49, 77, 167, 539, 1169, 1837, 8183, 12859, 90013.
What is 90013 in binary?
10101111110011101 (hexadecimal 15F9D, octal 257635).
What is the square root of 90013?
About 300.0217, exactly 7√1837.
Is 90013 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 90013?
90013 is a happy number: repeatedly adding the squares of its digits reaches 1.