The number 83112
83112 is a composite number with 16 divisors. Its prime factorisation is × 3 × 3463. Divisors (16): 1, 2, 3, 4, 6, 8, 12, 24, 3463, 6926, 10389, 13852, 20778, 27704, 41556, 83112.
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How to work it out
- 1
What is special about 83112: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
83112 is composite. Its prime factorisation is
- 3
The divisors add up to 207840; without 83112 itself that is 124728, so 83112 is abundant (124728 is more than 83112). Euler's totient φ(83112) = 27696 numbers up to 83112 share no factor with it.
- 4
The digits of 83112 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83112 = 2^{3} \times 3 \times 3463 \]83112 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 207840 |
| Euler totient φ(n) | 27696 |
| Square | 6907604544 |
| Cube | 574104828860928 |
| Square root | 288.291519 (= 2√20778) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 151 |
| Scientific notation | 8.3112 × |
83112 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand one hundred and twelve |
| Binary (base 2) | 10100010010101000 |
| Octal (base 8) | 242250 |
| Hexadecimal (base 16) | 144A8 |
| Base 3 | 11020000020 |
| As time | 83112 seconds = 23 h 5 min 12 s |
Is 83112 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83112 ÷ 2 = 41556) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83112 ÷ 3 = 27704) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83112 ÷ 4 = 20778) | 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 (83112 ÷ 6 = 13852) | 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 (83112 ÷ 8 = 10389) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83112 ÷ 12 = 6926) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83112 a prime number?
No. 83112 = × 3 × 3463, so it is divisible by 2.
What are the factors of 83112?
1, 2, 3, 4, 6, 8, 12, 24, 3463, 6926, 10389, 13852, 20778, 27704, 41556, 83112.
What is 83112 in binary?
10100010010101000 (hexadecimal 144A8, octal 242250).
What is the square root of 83112?
About 288.2915, exactly 2√20778.
Is 83112 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 83112?
83112 is a happy number: repeatedly adding the squares of its digits reaches 1.