The number 1748
1748 is a composite number with 12 divisors. Its prime factorisation is × 19 × 23. Divisors (12): 1, 2, 4, 19, 23, 38, 46, 76, 92, 437, 874, 1748.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1748: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1748 is composite. Its prime factorisation is
- 3
The divisors add up to 3360; without 1748 itself that is 1612, so 1748 is deficient (1612 is less than 1748). Euler's totient φ(1748) = 792 numbers up to 1748 share no factor with it.
- 4
The digits of 1748 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 117 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1748 = 2^{2} \times 19 \times 23 \]1748 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 3360 |
| Euler totient φ(n) | 792 |
| Square | 3055504 |
| Cube | 5341020992 |
| Square root | 41.809090 (= 2√437) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 117 |
| Scientific notation | 1.748 × |
1748 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and forty-eight |
| Roman numerals | MDCCXLVIII |
| Binary (base 2) | 11011010100 |
| Octal (base 8) | 3324 |
| Hexadecimal (base 16) | 6D4 |
| Base 3 | 2101202 |
| As time | 1748 seconds = 29 min 8 s |
Is 1748 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1748 ÷ 2 = 874) | 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 (1748 ÷ 4 = 437) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | 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 1748 a prime number?
No. 1748 = × 19 × 23, so it is divisible by 2.
What are the factors of 1748?
1, 2, 4, 19, 23, 38, 46, 76, 92, 437, 874, 1748.
What is 1748 in binary?
11011010100 (hexadecimal 6D4, octal 3324).
What is the square root of 1748?
About 41.8091, exactly 2√437.
What is 1748 in Roman numerals?
MDCCXLVIII.
Is 1748 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 1748?
1748 is a happy number: repeatedly adding the squares of its digits reaches 1.