The number 1644
1644 is a composite number with 12 divisors. Its prime factorisation is × 3 × 137. Divisors (12): 1, 2, 3, 4, 6, 12, 137, 274, 411, 548, 822, 1644.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1644 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1644 is composite. Its prime factorisation is
- 3
The divisors add up to 3864; without 1644 itself that is 2220, so 1644 is abundant (2220 is more than 1644). Euler's totient φ(1644) = 544 numbers up to 1644 share no factor with it.
- 4
The digits of 1644 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1644 = 2^{2} \times 3 \times 137 \]1644 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 3864 |
| Euler totient φ(n) | 544 |
| Square | 2702736 |
| Cube | 4443297984 |
| Square root | 40.546270 (= 2√411) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 135 |
| Scientific notation | 1.644 × |
1644 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and forty-four |
| Roman numerals | MDCXLIV |
| Binary (base 2) | 11001101100 |
| Octal (base 8) | 3154 |
| Hexadecimal (base 16) | 66C |
| Base 3 | 2020220 |
| As time | 1644 seconds = 27 min 24 s |
Is 1644 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1644 ÷ 2 = 822) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1644 ÷ 3 = 548) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1644 ÷ 4 = 411) | 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 | Yes (1644 ÷ 6 = 274) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 4) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1644 ÷ 12 = 137) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1644 a prime number?
No. 1644 = × 3 × 137, so it is divisible by 2.
What are the factors of 1644?
1, 2, 3, 4, 6, 12, 137, 274, 411, 548, 822, 1644.
What is 1644 in binary?
11001101100 (hexadecimal 66C, octal 3154).
What is the square root of 1644?
About 40.5463, exactly 2√411.
What is 1644 in Roman numerals?
MDCXLIV.
Is 1644 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 1644?
It is a composite number with 12 divisors.