The number 38448
38448 is a composite number with 40 divisors. Its prime factorisation is × × 89. Divisors (40): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72 … 38448.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 38448: a Harshad number: divisible by its digit sum 27.
- 2
38448 is composite. Its prime factorisation is
- 3
The divisors add up to 111600; without 38448 itself that is 73152, so 38448 is abundant (73152 is more than 38448). Euler's totient φ(38448) = 12672 numbers up to 38448 share no factor with it.
- 4
The digits of 38448 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 38448 = 2^{4} \times 3^{3} \times 89 \]38448 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 111600 |
| Euler totient φ(n) | 12672 |
| Square | 1478248704 |
| Cube | 56835706171392 |
| Square root | 196.081616 (= 12√267) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 62 |
| Scientific notation | 3.8448 × |
38448 in other forms
| Form | Value |
|---|---|
| In words | thirty-eight thousand four hundred and forty-eight |
| Binary (base 2) | 1001011000110000 |
| Octal (base 8) | 113060 |
| Hexadecimal (base 16) | 9630 |
| Base 3 | 1221202000 |
| As time | 38448 seconds = 10 h 40 min 48 s |
Is 38448 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (38448 ÷ 2 = 19224) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (38448 ÷ 3 = 12816) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (38448 ÷ 4 = 9612) | 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 (38448 ÷ 6 = 6408) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (38448 ÷ 8 = 4806) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (38448 ÷ 9 = 4272) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (38448 ÷ 12 = 3204) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 38448 a prime number?
No. 38448 = × × 89, so it is divisible by 2.
What are the factors of 38448?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 89, 108, 144, 178, 216, 267, 356, 432, 534, 712, 801, 1068, 1424, 1602, 2136, 2403, 3204, 4272, 4806, 6408, 9612, 12816, 19224, 38448.
What is 38448 in binary?
1001011000110000 (hexadecimal 9630, octal 113060).
What is the square root of 38448?
About 196.0816, exactly 12√267.
Is 38448 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 38448?
38448 is a Harshad number: divisible by its digit sum 27.