The number 1746
1746 is a composite number with 12 divisors. Its prime factorisation is 2 × × 97. Divisors (12): 1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873, 1746.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1746: a Harshad number: divisible by its digit sum 18.
- 2
1746 is composite. Its prime factorisation is
- 3
The divisors add up to 3822; without 1746 itself that is 2076, so 1746 is abundant (2076 is more than 1746). Euler's totient φ(1746) = 576 numbers up to 1746 share no factor with it.
- 4
The digits of 1746 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 148 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1746 = 2 \times 3^{2} \times 97 \]1746 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 3822 |
| Euler totient φ(n) | 576 |
| Square | 3048516 |
| Cube | 5322708936 |
| Square root | 41.785165 (= 3√194) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 148 |
| Scientific notation | 1.746 × |
1746 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and forty-six |
| Roman numerals | MDCCXLVI |
| Binary (base 2) | 11011010010 |
| Octal (base 8) | 3322 |
| Hexadecimal (base 16) | 6D2 |
| Base 3 | 2101200 |
| As time | 1746 seconds = 29 min 6 s |
Is 1746 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1746 ÷ 2 = 873) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1746 ÷ 3 = 582) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1746 ÷ 6 = 291) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1746 ÷ 9 = 194) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1746 a prime number?
No. 1746 = 2 × × 97, so it is divisible by 2.
What are the factors of 1746?
1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873, 1746.
What is 1746 in binary?
11011010010 (hexadecimal 6D2, octal 3322).
What is the square root of 1746?
About 41.7852, exactly 3√194.
What is 1746 in Roman numerals?
MDCCXLVI.
Is 1746 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 1746?
1746 is a Harshad number: divisible by its digit sum 18.