The number 9012
9012 is a composite number with 12 divisors. Its prime factorisation is × 3 × 751. Divisors (12): 1, 2, 3, 4, 6, 12, 751, 1502, 2253, 3004, 4506, 9012.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9012: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.
- 2
9012 is composite. Its prime factorisation is
- 3
The divisors add up to 21056; without 9012 itself that is 12044, so 9012 is abundant (12044 is more than 9012). Euler's totient φ(9012) = 3000 numbers up to 9012 share no factor with it.
- 4
The digits of 9012 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 47 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9012 = 2^{2} \times 3 \times 751 \]9012 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 21056 |
| Euler totient φ(n) | 3000 |
| Square | 81216144 |
| Cube | 731919889728 |
| Square root | 94.931554 (= 2√2253) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 47 |
| Scientific notation | 9.012 × |
9012 in other forms
| Form | Value |
|---|---|
| In words | nine thousand and twelve |
| Binary (base 2) | 10001100110100 |
| Octal (base 8) | 21464 |
| Hexadecimal (base 16) | 2334 |
| Base 3 | 110100210 |
| As time | 9012 seconds = 2 h 30 min 12 s |
Is 9012 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9012 ÷ 2 = 4506) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9012 ÷ 3 = 3004) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9012 ÷ 4 = 2253) | 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 (9012 ÷ 6 = 1502) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (9012 ÷ 12 = 751) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9012 a prime number?
No. 9012 = × 3 × 751, so it is divisible by 2.
What are the factors of 9012?
1, 2, 3, 4, 6, 12, 751, 1502, 2253, 3004, 4506, 9012.
What is 9012 in binary?
10001100110100 (hexadecimal 2334, octal 21464).
What is the square root of 9012?
About 94.9316, exactly 2√2253.
Is 9012 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 9012?
9012 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 12.