The number 1051
1051 is a twin prime (1049 and 1051 are both prime) and the 177th prime number. Its only divisors are 1 and 1051.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1051: a twin prime (1049 and 1051 are both prime); the 177th prime number.
- 2
1051 is prime, so its only factors are 1 and 1051. It is the 177th prime; the next prime is 1061 and the one before is 1049.
- 3
The divisors add up to 1052; without 1051 itself that is 1, so 1051 is deficient (1 is less than 1051). Euler's totient φ(1051) = 1050 numbers up to 1051 share no factor with it.
- 4
The digits of 1051 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 93 steps to reach 1.
1051 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1052 |
| Euler totient φ(n) | 1050 |
| Square | 1104601 |
| Cube | 1160935651 |
| Square root | 32.419130 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 93 |
| Scientific notation | 1.051 × |
1051 in other forms
| Form | Value |
|---|---|
| In words | one thousand and fifty-one |
| Roman numerals | MLI |
| Binary (base 2) | 10000011011 |
| Octal (base 8) | 2033 |
| Hexadecimal (base 16) | 41B |
| Base 3 | 1102221 |
| As time | 1051 seconds = 17 min 31 s |
Is 1051 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 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | 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 | No (remainder 1) | 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 3) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | 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 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1051 a prime number?
Yes. 1051 is divisible only by 1 and itself.
What are the factors of 1051?
1, 1051.
What is 1051 in binary?
10000011011 (hexadecimal 41B, octal 2033).
What is the square root of 1051?
About 32.4191.
What is 1051 in Roman numerals?
MLI.
Is 1051 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 1051?
1051 is a twin prime (1049 and 1051 are both prime); the 177th prime number.