The number 1054
1054 is a composite number with 8 divisors. Its prime factorisation is 2 × 17 × 31. Divisors (8): 1, 2, 17, 31, 34, 62, 527, 1054.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1054 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1054 is composite. Its prime factorisation is
- 3
The divisors add up to 1728; without 1054 itself that is 674, so 1054 is deficient (674 is less than 1054). Euler's totient φ(1054) = 480 numbers up to 1054 share no factor with it.
- 4
The digits of 1054 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 80 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1054 = 2 \times 17 \times 31 \]
1054 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1728 |
| Euler totient φ(n) | 480 |
| Square | 1110916 |
| Cube | 1170905464 |
| Square root | 32.465366 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 80 |
| Scientific notation | 1.054 × |
1054 in other forms
| Form | Value |
|---|---|
| In words | one thousand and fifty-four |
| Roman numerals | MLIV |
| Binary (base 2) | 10000011110 |
| Octal (base 8) | 2036 |
| Hexadecimal (base 16) | 41E |
| Base 3 | 1110001 |
| As time | 1054 seconds = 17 min 34 s |
Is 1054 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1054 ÷ 2 = 527) | 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 2) | 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 4) | 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 6) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1054 a prime number?
No. 1054 = 2 × 17 × 31, so it is divisible by 2.
What are the factors of 1054?
1, 2, 17, 31, 34, 62, 527, 1054.
What is 1054 in binary?
10000011110 (hexadecimal 41E, octal 2036).
What is the square root of 1054?
About 32.4654.
What is 1054 in Roman numerals?
MLIV.
Is 1054 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 1054?
It is a composite number with 8 divisors.