The number 1029
1029 is a composite number with 8 divisors. Its prime factorisation is 3 × . Divisors (8): 1, 3, 7, 21, 49, 147, 343, 1029.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1029: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
1029 is composite. Its prime factorisation is
- 3
The divisors add up to 1600; without 1029 itself that is 571, so 1029 is deficient (571 is less than 1029). Euler's totient φ(1029) = 588 numbers up to 1029 share no factor with it.
- 4
The digits of 1029 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 124 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1029 = 3 \times 7^{3} \]1029 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1600 |
| Euler totient φ(n) | 588 |
| Square | 1058841 |
| Cube | 1089547389 |
| Square root | 32.078030 (= 7√21) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 124 |
| Scientific notation | 1.029 × |
1029 in other forms
| Form | Value |
|---|---|
| In words | one thousand and twenty-nine |
| Roman numerals | MXXIX |
| Binary (base 2) | 10000000101 |
| Octal (base 8) | 2005 |
| Hexadecimal (base 16) | 405 |
| Base 3 | 1102010 |
| As time | 1029 seconds = 17 min 9 s |
Is 1029 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 | Yes (1029 ÷ 3 = 343) | 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 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1029 ÷ 7 = 147) | 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 5) | 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 | No (remainder 9) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1029 a prime number?
No. 1029 = 3 × , so it is divisible by 3.
What are the factors of 1029?
1, 3, 7, 21, 49, 147, 343, 1029.
What is 1029 in binary?
10000000101 (hexadecimal 405, octal 2005).
What is the square root of 1029?
About 32.0780, exactly 7√21.
What is 1029 in Roman numerals?
MXXIX.
Is 1029 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1029?
1029 is a happy number: repeatedly adding the squares of its digits reaches 1.