The number 1740
1740 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 29. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116 … 1740.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1740: a Harshad number: divisible by its digit sum 12.
- 2
1740 is composite. Its prime factorisation is
- 3
The divisors add up to 5040; without 1740 itself that is 3300, so 1740 is abundant (3300 is more than 1740). Euler's totient φ(1740) = 448 numbers up to 1740 share no factor with it.
- 4
The digits of 1740 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1740 = 2^{2} \times 3 \times 5 \times 29 \]1740 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 5040 |
| Euler totient φ(n) | 448 |
| Square | 3027600 |
| Cube | 5268024000 |
| Square root | 41.713307 (= 2√435) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 29 |
| Scientific notation | 1.74 × |
1740 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and forty |
| Roman numerals | MDCCXL |
| Binary (base 2) | 11011001100 |
| Octal (base 8) | 3314 |
| Hexadecimal (base 16) | 6CC |
| Base 3 | 2101110 |
| As time | 1740 seconds = 29 min 0 s |
Is 1740 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1740 ÷ 2 = 870) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1740 ÷ 3 = 580) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1740 ÷ 4 = 435) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1740 ÷ 5 = 348) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1740 ÷ 6 = 290) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1740 ÷ 10 = 174) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1740 ÷ 12 = 145) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1740 a prime number?
No. 1740 = × 3 × 5 × 29, so it is divisible by 2.
What are the factors of 1740?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116, 145, 174, 290, 348, 435, 580, 870, 1740.
What is 1740 in binary?
11011001100 (hexadecimal 6CC, octal 3314).
What is the square root of 1740?
About 41.7133, exactly 2√435.
What is 1740 in Roman numerals?
MDCCXL.
Is 1740 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1740?
1740 is a Harshad number: divisible by its digit sum 12.