The number 90480
90480 is a composite number with 80 divisors. Its prime factorisation is × 3 × 5 × 13 × 29. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 29 … 90480.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
90480 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
90480 is composite. Its prime factorisation is
- 3
The divisors add up to 312480; without 90480 itself that is 222000, so 90480 is abundant (222000 is more than 90480). Euler's totient φ(90480) = 21504 numbers up to 90480 share no factor with it.
- 4
The digits of 90480 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 115 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90480 = 2^{4} \times 3 \times 5 \times 13 \times 29 \]90480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 312480 |
| Euler totient φ(n) | 21504 |
| Square | 8186630400 |
| Cube | 740726318592000 |
| Square root | 300.798936 (= 4√5655) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 115 |
| Scientific notation | 9.048 × |
90480 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand four hundred and eighty |
| Binary (base 2) | 10110000101110000 |
| Octal (base 8) | 260560 |
| Hexadecimal (base 16) | 16170 |
| Base 3 | 11121010010 |
| As time | 90480 seconds = 25 h 8 min 0 s |
Is 90480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90480 ÷ 2 = 45240) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90480 ÷ 3 = 30160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90480 ÷ 4 = 22620) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (90480 ÷ 5 = 18096) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (90480 ÷ 6 = 15080) | 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 (90480 ÷ 8 = 11310) | 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 | Yes (90480 ÷ 10 = 9048) | 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 | Yes (90480 ÷ 12 = 7540) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90480 a prime number?
No. 90480 = × 3 × 5 × 13 × 29, so it is divisible by 2.
What are the factors of 90480?
1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 29, 30, 39, 40, 48, 52, 58, 60, 65, 78, 80, 87, 104, 116, 120, 130, 145, 156, 174, 195, 208, 232, 240, 260, 290, 312, 348, 377, 390, 435, 464, 520, 580, 624, 696, 754, 780, 870, 1040, 1131, 1160, 1392, 1508, 1560, 1740, 1885, 2262, 2320, 3016, 3120, 3480, 3770, 4524, 5655, 6032, 6960, 7540, 9048, 11310, 15080, 18096, 22620, 30160, 45240, 90480.
What is 90480 in binary?
10110000101110000 (hexadecimal 16170, octal 260560).
What is the square root of 90480?
About 300.7989, exactly 4√5655.
Is 90480 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 90480?
It is a composite number with 80 divisors.