The number 1729
1729 is a taxicab number: it is the sum of two cubes in 2 ways (1³ + 12³ and 9³ + 10³). Its prime factorisation is 7 × 13 × 19. Divisors (8): 1, 7, 13, 19, 91, 133, 247, 1729.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1729: a taxicab number: it is the sum of two cubes in 2 ways (1³ + 12³ and 9³ + 10³); a Harshad number: divisible by its digit sum 19.
- 2
1729 is composite. Its prime factorisation is
- 3
The divisors add up to 2240; without 1729 itself that is 511, so 1729 is deficient (511 is less than 1729). Euler's totient φ(1729) = 1296 numbers up to 1729 share no factor with it.
- 4
The digits of 1729 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 104 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1729 = 7 \times 13 \times 19 \]
1729 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 2240 |
| Euler totient φ(n) | 1296 |
| Square | 2989441 |
| Cube | 5168743489 |
| Square root | 41.581246 |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 104 |
| Scientific notation | 1.729 × |
1729 in other forms
| Form | Value |
|---|---|
| In words | one thousand seven hundred and twenty-nine |
| Roman numerals | MDCCXXIX |
| Binary (base 2) | 11011000001 |
| Octal (base 8) | 3301 |
| Hexadecimal (base 16) | 6C1 |
| Base 3 | 2101001 |
| As time | 1729 seconds = 28 min 49 s |
Is 1729 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | 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 | No (remainder 1) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1729 ÷ 7 = 247) | 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 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | 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 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1729 a prime number?
No. 1729 = 7 × 13 × 19, so it is divisible by 7.
What are the factors of 1729?
1, 7, 13, 19, 91, 133, 247, 1729.
What is 1729 in binary?
11011000001 (hexadecimal 6C1, octal 3301).
What is the square root of 1729?
About 41.5812.
What is 1729 in Roman numerals?
MDCCXXIX.
Is 1729 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 1729?
1729 is a taxicab number: it is the sum of two cubes in 2 ways (1³ + 12³ and 9³ + 10³); a Harshad number: divisible by its digit sum 19.