The number 90012
90012 is a composite number with 24 divisors. Its prime factorisation is × 3 × 13 × 577. Divisors (24): 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 577, 1154, 1731, 2308 … 90012.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90012: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
90012 is composite. Its prime factorisation is
- 3
The divisors add up to 226576; without 90012 itself that is 136564, so 90012 is abundant (136564 is more than 90012). Euler's totient φ(90012) = 27648 numbers up to 90012 share no factor with it.
- 4
The digits of 90012 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 164 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90012 = 2^{2} \times 3 \times 13 \times 577 \]90012 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 226576 |
| Euler totient φ(n) | 27648 |
| Square | 8102160144 |
| Cube | 729291638881728 |
| Square root | 300.019999 (= 2√22503) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 164 |
| Scientific notation | 9.0012 × |
90012 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand and twelve |
| Binary (base 2) | 10101111110011100 |
| Octal (base 8) | 257634 |
| Hexadecimal (base 16) | 15F9C |
| Base 3 | 11120110210 |
| As time | 90012 seconds = 25 h 0 min 12 s |
Is 90012 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90012 ÷ 2 = 45006) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (90012 ÷ 3 = 30004) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90012 ÷ 4 = 22503) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (90012 ÷ 6 = 15002) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 | No (remainder 4) | 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 2) | 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 (90012 ÷ 12 = 7501) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90012 a prime number?
No. 90012 = × 3 × 13 × 577, so it is divisible by 2.
What are the factors of 90012?
1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 577, 1154, 1731, 2308, 3462, 6924, 7501, 15002, 22503, 30004, 45006, 90012.
What is 90012 in binary?
10101111110011100 (hexadecimal 15F9C, octal 257634).
What is the square root of 90012?
About 300.0200, exactly 2√22503.
Is 90012 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 90012?
90012 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.