The number 15648
15648 is a composite number with 24 divisors. Its prime factorisation is × 3 × 163. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 163, 326, 489, 652 … 15648.
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How to work it out
- 1
What is special about 15648: a Harshad number: divisible by its digit sum 24.
- 2
15648 is composite. Its prime factorisation is
- 3
The divisors add up to 41328; without 15648 itself that is 25680, so 15648 is abundant (25680 is more than 15648). Euler's totient φ(15648) = 5184 numbers up to 15648 share no factor with it.
- 4
The digits of 15648 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 53 steps to reach 1.
LaTeX source of the formulas on this page
\[ 15648 = 2^{5} \times 3 \times 163 \]15648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 41328 |
| Euler totient φ(n) | 5184 |
| Square | 244859904 |
| Cube | 3831567777792 |
| Square root | 125.091966 (= 4√978) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 53 |
| Scientific notation | 1.5648 × |
15648 in other forms
| Form | Value |
|---|---|
| In words | fifteen thousand six hundred and forty-eight |
| Binary (base 2) | 11110100100000 |
| Octal (base 8) | 36440 |
| Hexadecimal (base 16) | 3D20 |
| Base 3 | 210110120 |
| As time | 15648 seconds = 4 h 20 min 48 s |
Is 15648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (15648 ÷ 2 = 7824) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (15648 ÷ 3 = 5216) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (15648 ÷ 4 = 3912) | 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 (15648 ÷ 6 = 2608) | 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 (15648 ÷ 8 = 1956) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (15648 ÷ 12 = 1304) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 15648 a prime number?
No. 15648 = × 3 × 163, so it is divisible by 2.
What are the factors of 15648?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 163, 326, 489, 652, 978, 1304, 1956, 2608, 3912, 5216, 7824, 15648.
What is 15648 in binary?
11110100100000 (hexadecimal 3D20, octal 36440).
What is the square root of 15648?
About 125.0920, exactly 4√978.
Is 15648 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 15648?
15648 is a Harshad number: divisible by its digit sum 24.