The number 1724
1724 is a composite number with 6 divisors. Its prime factorisation is × 431. Divisors (6): 1, 2, 4, 431, 862, 1724.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1724: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1724 is composite. Its prime factorisation is
- 3
The divisors add up to 3024; without 1724 itself that is 1300, so 1724 is deficient (1300 is less than 1724). Euler's totient φ(1724) = 860 numbers up to 1724 share no factor with it.
- 4
The digits of 1724 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1724 = 2^{2} \times 431 \]1724 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 6 |
| Sum of divisors | 3024 |
| Euler totient φ(n) | 860 |
| Square | 2972176 |
| Cube | 5124031424 |
| Square root | 41.521079 (= 2√431) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.724 × |
1724 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and twenty-four |
| Roman numerals | MDCCXXIV |
| Binary (base 2) | 11010111100 |
| Octal (base 8) | 3274 |
| Hexadecimal (base 16) | 6BC |
| Base 3 | 2100212 |
| As time | 1724 seconds = 28 min 44 s |
Is 1724 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1724 ÷ 2 = 862) | 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 (1724 ÷ 4 = 431) | 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 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 5) | 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 8) | 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 1724 a prime number?
No. 1724 = × 431, so it is divisible by 2.
What are the factors of 1724?
1, 2, 4, 431, 862, 1724.
What is 1724 in binary?
11010111100 (hexadecimal 6BC, octal 3274).
What is the square root of 1724?
About 41.5211, exactly 2√431.
What is 1724 in Roman numerals?
MDCCXXIV.
Is 1724 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 1724?
1724 is a happy number: repeatedly adding the squares of its digits reaches 1.