The number 34112
34112 is a composite number with 28 divisors. Its prime factorisation is × 13 × 41. Divisors (28): 1, 2, 4, 8, 13, 16, 26, 32, 41, 52, 64, 82, 104, 164, 208, 328 … 34112.
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How to work it out
- 1
What is special about 34112: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
34112 is composite. Its prime factorisation is
- 3
The divisors add up to 74676; without 34112 itself that is 40564, so 34112 is abundant (40564 is more than 34112). Euler's totient φ(34112) = 15360 numbers up to 34112 share no factor with it.
- 4
The digits of 34112 add up to 11, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34112 = 2^{6} \times 13 \times 41 \]34112 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 74676 |
| Euler totient φ(n) | 15360 |
| Square | 1163628544 |
| Cube | 39693696892928 |
| Square root | 184.694342 (= 8√533) |
| Digit sum / digital root | 11 / 2 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.4112 × |
34112 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand one hundred and twelve |
| Binary (base 2) | 1000010101000000 |
| Octal (base 8) | 102500 |
| Hexadecimal (base 16) | 8540 |
| Base 3 | 1201210102 |
| As time | 34112 seconds = 9 h 28 min 32 s |
Is 34112 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34112 ÷ 2 = 17056) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (34112 ÷ 4 = 8528) | 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 | No (remainder 2) | 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 | Yes (34112 ÷ 8 = 4264) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | 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 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 34112 a prime number?
No. 34112 = × 13 × 41, so it is divisible by 2.
What are the factors of 34112?
1, 2, 4, 8, 13, 16, 26, 32, 41, 52, 64, 82, 104, 164, 208, 328, 416, 533, 656, 832, 1066, 1312, 2132, 2624, 4264, 8528, 17056, 34112.
What is 34112 in binary?
1000010101000000 (hexadecimal 8540, octal 102500).
What is the square root of 34112?
About 184.6943, exactly 8√533.
Is 34112 divisible by 3?
No. Its digits add up to 11, which is not a multiple of 3.
What is special about the number 34112?
34112 is a happy number: repeatedly adding the squares of its digits reaches 1.