The number 90048
90048 is a composite number with 56 divisors. Its prime factorisation is × 3 × 7 × 67. Divisors (56): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48 … 90048.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90048: a Harshad number: divisible by its digit sum 21.
- 2
90048 is composite. Its prime factorisation is
- 3
The divisors add up to 276352; without 90048 itself that is 186304, so 90048 is abundant (186304 is more than 90048). Euler's totient φ(90048) = 25344 numbers up to 90048 share no factor with it.
- 4
The digits of 90048 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 177 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90048 = 2^{6} \times 3 \times 7 \times 67 \]90048 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 276352 |
| Euler totient φ(n) | 25344 |
| Square | 8108642304 |
| Cube | 730167022190592 |
| Square root | 300.079989 (= 8√1407) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 177 |
| Scientific notation | 9.0048 × |
90048 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand and forty-eight |
| Binary (base 2) | 10101111111000000 |
| Octal (base 8) | 257700 |
| Hexadecimal (base 16) | 15FC0 |
| Base 3 | 11120112010 |
| As time | 90048 seconds = 25 h 0 min 48 s |
Is 90048 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90048 ÷ 2 = 45024) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90048 ÷ 3 = 30016) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90048 ÷ 4 = 22512) | 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 | Yes (90048 ÷ 6 = 15008) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (90048 ÷ 7 = 12864) | 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 (90048 ÷ 8 = 11256) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 | Yes (90048 ÷ 12 = 7504) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90048 a prime number?
No. 90048 = × 3 × 7 × 67, so it is divisible by 2.
What are the factors of 90048?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 67, 84, 96, 112, 134, 168, 192, 201, 224, 268, 336, 402, 448, 469, 536, 672, 804, 938, 1072, 1344, 1407, 1608, 1876, 2144, 2814, 3216, 3752, 4288, 5628, 6432, 7504, 11256, 12864, 15008, 22512, 30016, 45024, 90048.
What is 90048 in binary?
10101111111000000 (hexadecimal 15FC0, octal 257700).
What is the square root of 90048?
About 300.0800, exactly 8√1407.
Is 90048 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 90048?
90048 is a Harshad number: divisible by its digit sum 21.