The number 48321
48321 is a composite number with 24 divisors. Its prime factorisation is × 7 × 13 × 59. Divisors (24): 1, 3, 7, 9, 13, 21, 39, 59, 63, 91, 117, 177, 273, 413, 531, 767 … 48321.
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How to work it out
- 1
What is special about 48321: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
48321 is composite. Its prime factorisation is
- 3
The divisors add up to 87360; without 48321 itself that is 39039, so 48321 is deficient (39039 is less than 48321). Euler's totient φ(48321) = 25056 numbers up to 48321 share no factor with it.
- 4
The digits of 48321 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 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48321 = 3^{2} \times 7 \times 13 \times 59 \]48321 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 87360 |
| Euler totient φ(n) | 25056 |
| Square | 2334919041 |
| Cube | 112825622980161 |
| Square root | 219.820381 (= 3√5369) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 44 |
| Scientific notation | 4.8321 × |
48321 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand three hundred and twenty-one |
| Binary (base 2) | 1011110011000001 |
| Octal (base 8) | 136301 |
| Hexadecimal (base 16) | BCC1 |
| Base 3 | 2110021200 |
| As time | 48321 seconds = 13 h 25 min 21 s |
Is 48321 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 (48321 ÷ 3 = 16107) | 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 | Yes (48321 ÷ 7 = 6903) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (48321 ÷ 9 = 5369) | 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 9) | 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 48321 a prime number?
No. 48321 = × 7 × 13 × 59, so it is divisible by 3.
What are the factors of 48321?
1, 3, 7, 9, 13, 21, 39, 59, 63, 91, 117, 177, 273, 413, 531, 767, 819, 1239, 2301, 3717, 5369, 6903, 16107, 48321.
What is 48321 in binary?
1011110011000001 (hexadecimal BCC1, octal 136301).
What is the square root of 48321?
About 219.8204, exactly 3√5369.
Is 48321 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 48321?
48321 is a happy number: repeatedly adding the squares of its digits reaches 1.