The number 1053
1053 is a composite number with 10 divisors. Its prime factorisation is × 13. Divisors (10): 1, 3, 9, 13, 27, 39, 81, 117, 351, 1053.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1053: a Harshad number: divisible by its digit sum 9.
- 2
1053 is composite. Its prime factorisation is
- 3
The divisors add up to 1694; without 1053 itself that is 641, so 1053 is deficient (641 is less than 1053). Euler's totient φ(1053) = 648 numbers up to 1053 share no factor with it.
- 4
The digits of 1053 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 80 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1053 = 3^{4} \times 13 \]1053 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 1694 |
| Euler totient φ(n) | 648 |
| Square | 1108809 |
| Cube | 1167575877 |
| Square root | 32.449961 (= 9√13) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 80 |
| Scientific notation | 1.053 × |
1053 in other forms
| Form | Value |
|---|---|
| In words | one thousand and fifty-three |
| Roman numerals | MLIII |
| Binary (base 2) | 10000011101 |
| Octal (base 8) | 2035 |
| Hexadecimal (base 16) | 41D |
| Base 3 | 1110000 |
| As time | 1053 seconds = 17 min 33 s |
Is 1053 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 (1053 ÷ 3 = 351) | 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 3) | 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 | No (remainder 3) | 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 | Yes (1053 ÷ 9 = 117) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 3) | 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 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1053 a prime number?
No. 1053 = × 13, so it is divisible by 3.
What are the factors of 1053?
1, 3, 9, 13, 27, 39, 81, 117, 351, 1053.
What is 1053 in binary?
10000011101 (hexadecimal 41D, octal 2035).
What is the square root of 1053?
About 32.4500, exactly 9√13.
What is 1053 in Roman numerals?
MLIII.
Is 1053 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1053?
1053 is a Harshad number: divisible by its digit sum 9.