The number 83421
83421 is a composite number with 24 divisors. Its prime factorisation is × 13 × 23 × 31. Divisors (24): 1, 3, 9, 13, 23, 31, 39, 69, 93, 117, 207, 279, 299, 403, 713, 897 … 83421.
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How to work it out
- 1
What is special about 83421: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
83421 is composite. Its prime factorisation is
- 3
The divisors add up to 139776; without 83421 itself that is 56355, so 83421 is deficient (56355 is less than 83421). Euler's totient φ(83421) = 47520 numbers up to 83421 share no factor with it.
- 4
The digits of 83421 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83421 = 3^{2} \times 13 \times 23 \times 31 \]83421 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 139776 |
| Euler totient φ(n) | 47520 |
| Square | 6959063241 |
| Cube | 580532014627461 |
| Square root | 288.826938 (= 3√9269) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 112 |
| Scientific notation | 8.3421 × |
83421 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand four hundred and twenty-one |
| Binary (base 2) | 10100010111011101 |
| Octal (base 8) | 242735 |
| Hexadecimal (base 16) | 145DD |
| Base 3 | 11020102200 |
| As time | 83421 seconds = 23 h 10 min 21 s |
Is 83421 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83421 ÷ 3 = 27807) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | 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 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | No (remainder 5) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (83421 ÷ 9 = 9269) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 83421 a prime number?
No. 83421 = × 13 × 23 × 31, so it is divisible by 3.
What are the factors of 83421?
1, 3, 9, 13, 23, 31, 39, 69, 93, 117, 207, 279, 299, 403, 713, 897, 1209, 2139, 2691, 3627, 6417, 9269, 27807, 83421.
What is 83421 in binary?
10100010111011101 (hexadecimal 145DD, octal 242735).
What is the square root of 83421?
About 288.8269, exactly 3√9269.
Is 83421 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 83421?
83421 is a happy number: repeatedly adding the squares of its digits reaches 1.