The number 3648
3648 is a composite number with 28 divisors. Its prime factorisation is × 3 × 19. Divisors (28): 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76 … 3648.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
3648 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
3648 is composite. Its prime factorisation is
- 3
The divisors add up to 10160; without 3648 itself that is 6512, so 3648 is abundant (6512 is more than 3648). Euler's totient φ(3648) = 1152 numbers up to 3648 share no factor with it.
- 4
The digits of 3648 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 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 3648 = 2^{6} \times 3 \times 19 \]3648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 10160 |
| Euler totient φ(n) | 1152 |
| Square | 13307904 |
| Cube | 48547233792 |
| Square root | 60.398675 (= 8√57) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 38 |
| Scientific notation | 3.648 × |
3648 in other forms
| Form | Value |
|---|---|
| In words | three thousand six hundred and forty-eight |
| Roman numerals | MMMDCXLVIII |
| Binary (base 2) | 111001000000 |
| Octal (base 8) | 7100 |
| Hexadecimal (base 16) | E40 |
| Base 3 | 12000010 |
| As time | 3648 seconds = 1 h 0 min 48 s |
Is 3648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (3648 ÷ 2 = 1824) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (3648 ÷ 3 = 1216) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (3648 ÷ 4 = 912) | 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 (3648 ÷ 6 = 608) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (3648 ÷ 8 = 456) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (3648 ÷ 12 = 304) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 3648 a prime number?
No. 3648 = × 3 × 19, so it is divisible by 2.
What are the factors of 3648?
1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76, 96, 114, 152, 192, 228, 304, 456, 608, 912, 1216, 1824, 3648.
What is 3648 in binary?
111001000000 (hexadecimal E40, octal 7100).
What is the square root of 3648?
About 60.3987, exactly 8√57.
What is 3648 in Roman numerals?
MMMDCXLVIII.
Is 3648 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 3648?
It is a composite number with 28 divisors.