The number 1744
1744 is a composite number with 10 divisors. Its prime factorisation is × 109. Divisors (10): 1, 2, 4, 8, 16, 109, 218, 436, 872, 1744.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1744: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.
- 2
1744 is composite. Its prime factorisation is
- 3
The divisors add up to 3410; without 1744 itself that is 1666, so 1744 is deficient (1666 is less than 1744). Euler's totient φ(1744) = 864 numbers up to 1744 share no factor with it.
- 4
The digits of 1744 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 117 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1744 = 2^{4} \times 109 \]1744 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 3410 |
| Euler totient φ(n) | 864 |
| Square | 3041536 |
| Cube | 5304438784 |
| Square root | 41.761226 (= 4√109) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 117 |
| Scientific notation | 1.744 × |
1744 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and forty-four |
| Roman numerals | MDCCXLIV |
| Binary (base 2) | 11011010000 |
| Octal (base 8) | 3320 |
| Hexadecimal (base 16) | 6D0 |
| Base 3 | 2101121 |
| As time | 1744 seconds = 29 min 4 s |
Is 1744 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1744 ÷ 2 = 872) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1744 ÷ 4 = 436) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | Yes (1744 ÷ 8 = 218) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1744 a prime number?
No. 1744 = × 109, so it is divisible by 2.
What are the factors of 1744?
1, 2, 4, 8, 16, 109, 218, 436, 872, 1744.
What is 1744 in binary?
11011010000 (hexadecimal 6D0, octal 3320).
What is the square root of 1744?
About 41.7612, exactly 4√109.
What is 1744 in Roman numerals?
MDCCXLIV.
Is 1744 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 1744?
1744 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 16.