The number 52320
52320 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 109. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 52320.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 52320: a Harshad number: divisible by its digit sum 12.
- 2
52320 is composite. Its prime factorisation is
- 3
The divisors add up to 166320; without 52320 itself that is 114000, so 52320 is abundant (114000 is more than 52320). Euler's totient φ(52320) = 13824 numbers up to 52320 share no factor with it.
- 4
The digits of 52320 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 47 steps to reach 1.
LaTeX source of the formulas on this page
\[ 52320 = 2^{5} \times 3 \times 5 \times 109 \]52320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 166320 |
| Euler totient φ(n) | 13824 |
| Square | 2737382400 |
| Cube | 143219847168000 |
| Square root | 228.735655 (= 4√3270) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 47 |
| Scientific notation | 5.232 × |
52320 in other forms
| Form | Value |
|---|---|
| In words | fifty-two thousand three hundred and twenty |
| Binary (base 2) | 1100110001100000 |
| Octal (base 8) | 146140 |
| Hexadecimal (base 16) | CC60 |
| Base 3 | 2122202210 |
| As time | 52320 seconds = 14 h 32 min 0 s |
Is 52320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (52320 ÷ 2 = 26160) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (52320 ÷ 3 = 17440) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (52320 ÷ 4 = 13080) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (52320 ÷ 5 = 10464) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (52320 ÷ 6 = 8720) | 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 | Yes (52320 ÷ 8 = 6540) | 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 | Yes (52320 ÷ 10 = 5232) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (52320 ÷ 12 = 4360) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 52320 a prime number?
No. 52320 = × 3 × 5 × 109, so it is divisible by 2.
What are the factors of 52320?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 109, 120, 160, 218, 240, 327, 436, 480, 545, 654, 872, 1090, 1308, 1635, 1744, 2180, 2616, 3270, 3488, 4360, 5232, 6540, 8720, 10464, 13080, 17440, 26160, 52320.
What is 52320 in binary?
1100110001100000 (hexadecimal CC60, octal 146140).
What is the square root of 52320?
About 228.7357, exactly 4√3270.
Is 52320 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 52320?
52320 is a Harshad number: divisible by its digit sum 12.