The number 1664
1664 is a composite number with 16 divisors. Its prime factorisation is × 13. Divisors (16): 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1664 is composite. Its prime factorisation is
- 3
The divisors add up to 3570; without 1664 itself that is 1906, so 1664 is abundant (1906 is more than 1664). Euler's totient φ(1664) = 768 numbers up to 1664 share no factor with it.
- 4
The digits of 1664 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 16 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1664 = 2^{7} \times 13 \]1664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 3570 |
| Euler totient φ(n) | 768 |
| Square | 2768896 |
| Cube | 4607442944 |
| Square root | 40.792156 (= 8√26) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 16 |
| Scientific notation | 1.664 × |
1664 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and sixty-four |
| Roman numerals | MDCLXIV |
| Binary (base 2) | 11010000000 |
| Octal (base 8) | 3200 |
| Hexadecimal (base 16) | 680 |
| Base 3 | 2021122 |
| As time | 1664 seconds = 27 min 44 s |
Is 1664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1664 ÷ 2 = 832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1664 ÷ 4 = 416) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (1664 ÷ 8 = 208) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1664 a prime number?
No. 1664 = × 13, so it is divisible by 2.
What are the factors of 1664?
1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664.
What is 1664 in binary?
11010000000 (hexadecimal 680, octal 3200).
What is the square root of 1664?
About 40.7922, exactly 8√26.
What is 1664 in Roman numerals?
MDCLXIV.
Is 1664 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 1664?
It is a composite number with 16 divisors.