The number 32448
32448 is a composite number with 42 divisors. Its prime factorisation is × 3 × . Divisors (42): 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64 … 32448.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 32448: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
32448 is composite. Its prime factorisation is
- 3
The divisors add up to 92964; without 32448 itself that is 60516, so 32448 is abundant (60516 is more than 32448). Euler's totient φ(32448) = 9984 numbers up to 32448 share no factor with it.
- 4
The digits of 32448 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 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 32448 = 2^{6} \times 3 \times 13^{2} \]32448 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 92964 |
| Euler totient φ(n) | 9984 |
| Square | 1052872704 |
| Cube | 34163613499392 |
| Square root | 180.133284 (= 104√3) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 41 |
| Scientific notation | 3.2448 × |
32448 in other forms
| Form | Value |
|---|---|
| In words | thirty-two thousand four hundred and forty-eight |
| Binary (base 2) | 111111011000000 |
| Octal (base 8) | 77300 |
| Hexadecimal (base 16) | 7EC0 |
| Base 3 | 1122111210 |
| As time | 32448 seconds = 9 h 0 min 48 s |
Is 32448 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (32448 ÷ 2 = 16224) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (32448 ÷ 3 = 10816) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (32448 ÷ 4 = 8112) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (32448 ÷ 6 = 5408) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (32448 ÷ 8 = 4056) | 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 8) | 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 | Yes (32448 ÷ 12 = 2704) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 32448 a prime number?
No. 32448 = × 3 × , so it is divisible by 2.
What are the factors of 32448?
1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 156, 169, 192, 208, 312, 338, 416, 507, 624, 676, 832, 1014, 1248, 1352, 2028, 2496, 2704, 4056, 5408, 8112, 10816, 16224, 32448.
What is 32448 in binary?
111111011000000 (hexadecimal 7EC0, octal 77300).
What is the square root of 32448?
About 180.1333, exactly 104√3.
Is 32448 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 32448?
32448 is a happy number: repeatedly adding the squares of its digits reaches 1.