The number 90040
90040 is a composite number with 16 divisors. Its prime factorisation is × 5 × 2251. Divisors (16): 1, 2, 4, 5, 8, 10, 20, 40, 2251, 4502, 9004, 11255, 18008, 22510, 45020, 90040.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90040: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
90040 is composite. Its prime factorisation is
- 3
The divisors add up to 202680; without 90040 itself that is 112640, so 90040 is abundant (112640 is more than 90040). Euler's totient φ(90040) = 36000 numbers up to 90040 share no factor with it.
- 4
The digits of 90040 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 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90040 = 2^{3} \times 5 \times 2251 \]90040 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 202680 |
| Euler totient φ(n) | 36000 |
| Square | 8107201600 |
| Cube | 729972432064000 |
| Square root | 300.066659 (= 2√22510) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 63 |
| Scientific notation | 9.004 × |
90040 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand and forty |
| Binary (base 2) | 10101111110111000 |
| Octal (base 8) | 257670 |
| Hexadecimal (base 16) | 15FB8 |
| Base 3 | 11120111211 |
| As time | 90040 seconds = 25 h 0 min 40 s |
Is 90040 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90040 ÷ 2 = 45020) | 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 | Yes (90040 ÷ 4 = 22510) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (90040 ÷ 5 = 18008) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 | Yes (90040 ÷ 8 = 11255) | 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 | Yes (90040 ÷ 10 = 9004) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90040 a prime number?
No. 90040 = × 5 × 2251, so it is divisible by 2.
What are the factors of 90040?
1, 2, 4, 5, 8, 10, 20, 40, 2251, 4502, 9004, 11255, 18008, 22510, 45020, 90040.
What is 90040 in binary?
10101111110111000 (hexadecimal 15FB8, octal 257670).
What is the square root of 90040?
About 300.0667, exactly 2√22510.
Is 90040 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 90040?
90040 is a happy number: repeatedly adding the squares of its digits reaches 1.