The number 90120
90120 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 751. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 90120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90120: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
90120 is composite. Its prime factorisation is
- 3
The divisors add up to 270720; without 90120 itself that is 180600, so 90120 is abundant (180600 is more than 90120). Euler's totient φ(90120) = 24000 numbers up to 90120 share no factor with it.
- 4
The digits of 90120 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90120 = 2^{3} \times 3 \times 5 \times 751 \]90120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 270720 |
| Euler totient φ(n) | 24000 |
| Square | 8121614400 |
| Cube | 731919889728000 |
| Square root | 300.199933 (= 2√22530) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 63 |
| Scientific notation | 9.012 × |
90120 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand one hundred and twenty |
| Binary (base 2) | 10110000000001000 |
| Octal (base 8) | 260010 |
| Hexadecimal (base 16) | 16008 |
| Base 3 | 11120121210 |
| As time | 90120 seconds = 25 h 2 min 0 s |
Is 90120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90120 ÷ 2 = 45060) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90120 ÷ 3 = 30040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90120 ÷ 4 = 22530) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (90120 ÷ 5 = 18024) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (90120 ÷ 6 = 15020) | 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 (90120 ÷ 8 = 11265) | 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 (90120 ÷ 10 = 9012) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (90120 ÷ 12 = 7510) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90120 a prime number?
No. 90120 = × 3 × 5 × 751, so it is divisible by 2.
What are the factors of 90120?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 751, 1502, 2253, 3004, 3755, 4506, 6008, 7510, 9012, 11265, 15020, 18024, 22530, 30040, 45060, 90120.
What is 90120 in binary?
10110000000001000 (hexadecimal 16008, octal 260010).
What is the square root of 90120?
About 300.1999, exactly 2√22530.
Is 90120 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 90120?
90120 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.