The number 1647
1647 is a composite number with 8 divisors. Its prime factorisation is × 61. Divisors (8): 1, 3, 9, 27, 61, 183, 549, 1647.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1647 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1647 is composite. Its prime factorisation is
- 3
The divisors add up to 2480; without 1647 itself that is 833, so 1647 is deficient (833 is less than 1647). Euler's totient φ(1647) = 1080 numbers up to 1647 share no factor with it.
- 4
The digits of 1647 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 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1647 = 3^{3} \times 61 \]1647 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 2480 |
| Euler totient φ(n) | 1080 |
| Square | 2712609 |
| Cube | 4467667023 |
| Square root | 40.583248 (= 3√183) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 135 |
| Scientific notation | 1.647 × |
1647 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and forty-seven |
| Roman numerals | MDCXLVII |
| Binary (base 2) | 11001101111 |
| Octal (base 8) | 3157 |
| Hexadecimal (base 16) | 66F |
| Base 3 | 2021000 |
| As time | 1647 seconds = 27 min 27 s |
Is 1647 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1647 ÷ 3 = 549) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | No (remainder 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1647 ÷ 9 = 183) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1647 a prime number?
No. 1647 = × 61, so it is divisible by 3.
What are the factors of 1647?
1, 3, 9, 27, 61, 183, 549, 1647.
What is 1647 in binary?
11001101111 (hexadecimal 66F, octal 3157).
What is the square root of 1647?
About 40.5832, exactly 3√183.
What is 1647 in Roman numerals?
MDCXLVII.
Is 1647 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1647?
It is a composite number with 8 divisors.