The number 648
648 is a composite number with 20 divisors. Its prime factorisation is × . Divisors (20): 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108 … 648.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 648: a Harshad number: divisible by its digit sum 18.
- 2
648 is composite. Its prime factorisation is
- 3
The divisors add up to 1815; without 648 itself that is 1167, so 648 is abundant (1167 is more than 648). Euler's totient φ(648) = 216 numbers up to 648 share no factor with it.
- 4
The digits of 648 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 648 = 2^{3} \times 3^{4} \]648 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 1815 |
| Euler totient φ(n) | 216 |
| Square | 419904 |
| Cube | 272097792 |
| Square root | 25.455844 (= 18√2) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 25 |
| Scientific notation | 6.48 × |
648 in other forms
| Form | Value |
|---|---|
| In words | six hundred and forty-eight |
| Roman numerals | DCXLVIII |
| Binary (base 2) | 1010001000 |
| Octal (base 8) | 1210 |
| Hexadecimal (base 16) | 288 |
| Base 3 | 220000 |
| As time | 648 seconds = 10 min 48 s |
Is 648 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (648 ÷ 2 = 324) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (648 ÷ 3 = 216) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (648 ÷ 4 = 162) | 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 (648 ÷ 6 = 108) | 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 (648 ÷ 8 = 81) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (648 ÷ 9 = 72) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (648 ÷ 12 = 54) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 648 a prime number?
No. 648 = × , so it is divisible by 2.
What are the factors of 648?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648.
What is 648 in binary?
1010001000 (hexadecimal 288, octal 1210).
What is the square root of 648?
About 25.4558, exactly 18√2.
What is 648 in Roman numerals?
DCXLVIII.
Is 648 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 648?
648 is a Harshad number: divisible by its digit sum 18.