The number 83376
83376 is a composite number with 40 divisors. Its prime factorisation is × × 193. Divisors (40): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72 … 83376.
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How to work it out
- 1
What is special about 83376: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
83376 is composite. Its prime factorisation is
- 3
The divisors add up to 240560; without 83376 itself that is 157184, so 83376 is abundant (157184 is more than 83376). Euler's totient φ(83376) = 27648 numbers up to 83376 share no factor with it.
- 4
The digits of 83376 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83376 = 2^{4} \times 3^{3} \times 193 \]83376 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 240560 |
| Euler totient φ(n) | 27648 |
| Square | 6951557376 |
| Cube | 579593047781376 |
| Square root | 288.749026 (= 12√579) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 138 |
| Scientific notation | 8.3376 × |
83376 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand three hundred and seventy-six |
| Binary (base 2) | 10100010110110000 |
| Octal (base 8) | 242660 |
| Hexadecimal (base 16) | 145B0 |
| Base 3 | 11020101000 |
| As time | 83376 seconds = 23 h 9 min 36 s |
Is 83376 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83376 ÷ 2 = 41688) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83376 ÷ 3 = 27792) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83376 ÷ 4 = 20844) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (83376 ÷ 6 = 13896) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (83376 ÷ 8 = 10422) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (83376 ÷ 9 = 9264) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | 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 (83376 ÷ 12 = 6948) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83376 a prime number?
No. 83376 = × × 193, so it is divisible by 2.
What are the factors of 83376?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 193, 216, 386, 432, 579, 772, 1158, 1544, 1737, 2316, 3088, 3474, 4632, 5211, 6948, 9264, 10422, 13896, 20844, 27792, 41688, 83376.
What is 83376 in binary?
10100010110110000 (hexadecimal 145B0, octal 242660).
What is the square root of 83376?
About 288.7490, exactly 12√579.
Is 83376 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 83376?
83376 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.