The number 90144
90144 is a composite number with 36 divisors. Its prime factorisation is × × 313. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96 … 90144.
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How to work it out
- 1
What is special about 90144: a Harshad number: divisible by its digit sum 18.
- 2
90144 is composite. Its prime factorisation is
- 3
The divisors add up to 257166; without 90144 itself that is 167022, so 90144 is abundant (167022 is more than 90144). Euler's totient φ(90144) = 29952 numbers up to 90144 share no factor with it.
- 4
The digits of 90144 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90144 = 2^{5} \times 3^{2} \times 313 \]90144 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 257166 |
| Euler totient φ(n) | 29952 |
| Square | 8125940736 |
| Cube | 732504801705984 |
| Square root | 300.239904 (= 12√626) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 89 |
| Scientific notation | 9.0144 × |
90144 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand one hundred and forty-four |
| Binary (base 2) | 10110000000100000 |
| Octal (base 8) | 260040 |
| Hexadecimal (base 16) | 16020 |
| Base 3 | 11120122200 |
| As time | 90144 seconds = 25 h 2 min 24 s |
Is 90144 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90144 ÷ 2 = 45072) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90144 ÷ 3 = 30048) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90144 ÷ 4 = 22536) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (90144 ÷ 6 = 15024) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (90144 ÷ 8 = 11268) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (90144 ÷ 9 = 10016) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (90144 ÷ 12 = 7512) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90144 a prime number?
No. 90144 = × × 313, so it is divisible by 2.
What are the factors of 90144?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288, 313, 626, 939, 1252, 1878, 2504, 2817, 3756, 5008, 5634, 7512, 10016, 11268, 15024, 22536, 30048, 45072, 90144.
What is 90144 in binary?
10110000000100000 (hexadecimal 16020, octal 260040).
What is the square root of 90144?
About 300.2399, exactly 12√626.
Is 90144 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 90144?
90144 is a Harshad number: divisible by its digit sum 18.