The number 1057
1057 is a binary palindrome (10000100001). Its prime factorisation is 7 × 151. Divisors (4): 1, 7, 151, 1057.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1057: a binary palindrome (10000100001); a semiprime: 7 × 151, the product of two primes.
- 2
1057 is composite. Its prime factorisation is
- 3
The divisors add up to 1216; without 1057 itself that is 159, so 1057 is deficient (159 is less than 1057). Euler's totient φ(1057) = 900 numbers up to 1057 share no factor with it.
- 4
The digits of 1057 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 80 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1057 = 7 \times 151 \]
1057 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 1216 |
| Euler totient φ(n) | 900 |
| Square | 1117249 |
| Cube | 1180932193 |
| Square root | 32.511536 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 80 |
| Scientific notation | 1.057 × |
1057 in other forms
| Form | Value |
|---|---|
| In words | one thousand and fifty-seven |
| Roman numerals | MLVII |
| Binary (base 2) | 10000100001 |
| Octal (base 8) | 2041 |
| Hexadecimal (base 16) | 421 |
| Base 3 | 1110011 |
| As time | 1057 seconds = 17 min 37 s |
Is 1057 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 2) | 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 (1057 ÷ 7 = 151) | 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 4) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | 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 1057 a prime number?
No. 1057 = 7 × 151, so it is divisible by 7.
What are the factors of 1057?
1, 7, 151, 1057.
What is 1057 in binary?
10000100001 (hexadecimal 421, octal 2041).
What is the square root of 1057?
About 32.5115.
What is 1057 in Roman numerals?
MLVII.
Is 1057 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 1057?
1057 is a binary palindrome (10000100001); a semiprime: 7 × 151, the product of two primes.