The number 83424
83424 is a composite number with 48 divisors. Its prime factorisation is × 3 × 11 × 79. Divisors (48): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66 … 83424.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83424: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
83424 is composite. Its prime factorisation is
- 3
The divisors add up to 241920; without 83424 itself that is 158496, so 83424 is abundant (158496 is more than 83424). Euler's totient φ(83424) = 24960 numbers up to 83424 share no factor with it.
- 4
The digits of 83424 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 89 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83424 = 2^{5} \times 3 \times 11 \times 79 \]83424 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 241920 |
| Euler totient φ(n) | 24960 |
| Square | 6959563776 |
| Cube | 580594648449024 |
| Square root | 288.832131 (= 4√5214) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 89 |
| Scientific notation | 8.3424 × |
83424 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand four hundred and twenty-four |
| Binary (base 2) | 10100010111100000 |
| Octal (base 8) | 242740 |
| Hexadecimal (base 16) | 145E0 |
| Base 3 | 11020102210 |
| As time | 83424 seconds = 23 h 10 min 24 s |
Is 83424 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83424 ÷ 2 = 41712) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83424 ÷ 3 = 27808) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (83424 ÷ 4 = 20856) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (83424 ÷ 6 = 13904) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (83424 ÷ 8 = 10428) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (83424 ÷ 11 = 7584) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (83424 ÷ 12 = 6952) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83424 a prime number?
No. 83424 = × 3 × 11 × 79, so it is divisible by 2.
What are the factors of 83424?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 79, 88, 96, 132, 158, 176, 237, 264, 316, 352, 474, 528, 632, 869, 948, 1056, 1264, 1738, 1896, 2528, 2607, 3476, 3792, 5214, 6952, 7584, 10428, 13904, 20856, 27808, 41712, 83424.
What is 83424 in binary?
10100010111100000 (hexadecimal 145E0, octal 242740).
What is the square root of 83424?
About 288.8321, exactly 4√5214.
Is 83424 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 83424?
83424 is a happy number: repeatedly adding the squares of its digits reaches 1.