The number 1764
1764 is a perfect square (42²). Its prime factorisation is × × . Divisors (27): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63 … 1764.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1764: a perfect square (42²); a Harshad number: divisible by its digit sum 18.
- 2
1764 is composite. Its prime factorisation is
- 3
The divisors add up to 5187; without 1764 itself that is 3423, so 1764 is abundant (3423 is more than 1764). Euler's totient φ(1764) = 504 numbers up to 1764 share no factor with it.
- 4
The digits of 1764 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 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1764 = 2^{2} \times 3^{2} \times 7^{2} \]1764 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 27 |
| Sum of divisors | 5187 |
| Euler totient φ(n) | 504 |
| Square | 3111696 |
| Cube | 5489031744 |
| Square root | 42 |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.764 × |
| Perfect power |
1764 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and sixty-four |
| Roman numerals | MDCCLXIV |
| Binary (base 2) | 11011100100 |
| Octal (base 8) | 3344 |
| Hexadecimal (base 16) | 6E4 |
| Base 3 | 2102100 |
| As time | 1764 seconds = 29 min 24 s |
Is 1764 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1764 ÷ 2 = 882) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1764 ÷ 3 = 588) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1764 ÷ 4 = 441) | 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 (1764 ÷ 6 = 294) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1764 ÷ 7 = 252) | 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 | Yes (1764 ÷ 9 = 196) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1764 ÷ 12 = 147) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1764 a prime number?
No. 1764 = × × , so it is divisible by 2.
What are the factors of 1764?
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 252, 294, 441, 588, 882, 1764.
What is 1764 in binary?
11011100100 (hexadecimal 6E4, octal 3344).
What is the square root of 1764?
42, because 42 × 42 = 1764.
What is 1764 in Roman numerals?
MDCCLXIV.
Is 1764 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1764?
1764 is a perfect square (42²); a Harshad number: divisible by its digit sum 18.