The number 32112
32112 is a composite number with 30 divisors. Its prime factorisation is × × 223. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 223 … 32112.
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How to work it out
- 1
What is special about 32112: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
32112 is composite. Its prime factorisation is
- 3
The divisors add up to 90272; without 32112 itself that is 58160, so 32112 is abundant (58160 is more than 32112). Euler's totient φ(32112) = 10656 numbers up to 32112 share no factor with it.
- 4
The digits of 32112 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 46 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32112 = 2^{4} \times 3^{2} \times 223 \]32112 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 90272 |
| Euler totient φ(n) | 10656 |
| Square | 1031180544 |
| Cube | 33113269628928 |
| Square root | 179.198214 (= 12√223) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 46 |
| Scientific notation | 3.2112 × |
32112 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand one hundred and twelve |
| Binary (base 2) | 111110101110000 |
| Octal (base 8) | 76560 |
| Hexadecimal (base 16) | 7D70 |
| Base 3 | 1122001100 |
| As time | 32112 seconds = 8 h 55 min 12 s |
Is 32112 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32112 ÷ 2 = 16056) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32112 ÷ 3 = 10704) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32112 ÷ 4 = 8028) | 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 (32112 ÷ 6 = 5352) | 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 | Yes (32112 ÷ 8 = 4014) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (32112 ÷ 9 = 3568) | 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 (32112 ÷ 12 = 2676) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32112 a prime number?
No. 32112 = × × 223, so it is divisible by 2.
What are the factors of 32112?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 223, 446, 669, 892, 1338, 1784, 2007, 2676, 3568, 4014, 5352, 8028, 10704, 16056, 32112.
What is 32112 in binary?
111110101110000 (hexadecimal 7D70, octal 76560).
What is the square root of 32112?
About 179.1982, exactly 12√223.
Is 32112 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 32112?
32112 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.