The number 12132
12132 is a composite number with 18 divisors. Its prime factorisation is × × 337. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 337, 674, 1011, 1348, 2022, 3033, 4044 … 12132.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12132: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
12132 is composite. Its prime factorisation is
- 3
The divisors add up to 30758; without 12132 itself that is 18626, so 12132 is abundant (18626 is more than 12132). Euler's totient φ(12132) = 4032 numbers up to 12132 share no factor with it.
- 4
The digits of 12132 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12132 = 2^{2} \times 3^{2} \times 337 \]12132 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 30758 |
| Euler totient φ(n) | 4032 |
| Square | 147185424 |
| Cube | 1785653563968 |
| Square root | 110.145359 (= 6√337) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 24 |
| Scientific notation | 1.2132 × |
12132 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand one hundred and thirty-two |
| Binary (base 2) | 10111101100100 |
| Octal (base 8) | 27544 |
| Hexadecimal (base 16) | 2F64 |
| Base 3 | 121122100 |
| As time | 12132 seconds = 3 h 22 min 12 s |
Is 12132 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12132 ÷ 2 = 6066) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12132 ÷ 3 = 4044) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12132 ÷ 4 = 3033) | 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 (12132 ÷ 6 = 2022) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | Yes (12132 ÷ 9 = 1348) | 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 (12132 ÷ 12 = 1011) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12132 a prime number?
No. 12132 = × × 337, so it is divisible by 2.
What are the factors of 12132?
1, 2, 3, 4, 6, 9, 12, 18, 36, 337, 674, 1011, 1348, 2022, 3033, 4044, 6066, 12132.
What is 12132 in binary?
10111101100100 (hexadecimal 2F64, octal 27544).
What is the square root of 12132?
About 110.1454, exactly 6√337.
Is 12132 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 12132?
12132 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.