The number 90400
90400 is a composite number with 36 divisors. Its prime factorisation is × × 113. Divisors (36): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 113, 160 … 90400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90400: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
90400 is composite. Its prime factorisation is
- 3
The divisors add up to 222642; without 90400 itself that is 132242, so 90400 is abundant (132242 is more than 90400). Euler's totient φ(90400) = 35840 numbers up to 90400 share no factor with it.
- 4
The digits of 90400 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 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90400 = 2^{5} \times 5^{2} \times 113 \]90400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 222642 |
| Euler totient φ(n) | 35840 |
| Square | 8172160000 |
| Cube | 738763264000000 |
| Square root | 300.665928 (= 20√226) |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 89 |
| Scientific notation | 9.04 × |
90400 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand four hundred |
| Binary (base 2) | 10110000100100000 |
| Octal (base 8) | 260440 |
| Hexadecimal (base 16) | 16120 |
| Base 3 | 11121000011 |
| As time | 90400 seconds = 25 h 6 min 40 s |
Is 90400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90400 ÷ 2 = 45200) | 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 (90400 ÷ 4 = 22600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (90400 ÷ 5 = 18080) | 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 2) | 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 (90400 ÷ 8 = 11300) | 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 (90400 ÷ 10 = 9040) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | 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 90400 a prime number?
No. 90400 = × × 113, so it is divisible by 2.
What are the factors of 90400?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 113, 160, 200, 226, 400, 452, 565, 800, 904, 1130, 1808, 2260, 2825, 3616, 4520, 5650, 9040, 11300, 18080, 22600, 45200, 90400.
What is 90400 in binary?
10110000100100000 (hexadecimal 16120, octal 260440).
What is the square root of 90400?
About 300.6659, exactly 20√226.
Is 90400 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 90400?
90400 is a happy number: repeatedly adding the squares of its digits reaches 1.