The number 1021
1021 is a twin prime (1019 and 1021 are both prime) and the 172nd prime number. Its only divisors are 1 and 1021.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1021: a twin prime (1019 and 1021 are both prime); the 172nd prime number.
- 2
1021 is prime, so its only factors are 1 and 1021. It is the 172nd prime; the next prime is 1031 and the one before is 1019.
- 3
The divisors add up to 1022; without 1021 itself that is 1, so 1021 is deficient (1 is less than 1021). Euler's totient φ(1021) = 1020 numbers up to 1021 share no factor with it.
- 4
The digits of 1021 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
1021 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1022 |
| Euler totient φ(n) | 1020 |
| Square | 1042441 |
| Cube | 1064332261 |
| Square root | 31.953091 |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 49 |
| Scientific notation | 1.021 × |
1021 in other forms
| Form | Value |
|---|---|
| In words | one thousand and twenty-one |
| Roman numerals | MXXI |
| Binary (base 2) | 1111111101 |
| Octal (base 8) | 1775 |
| Hexadecimal (base 16) | 3FD |
| Base 3 | 1101211 |
| As time | 1021 seconds = 17 min 1 s |
Is 1021 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 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 6) | 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 4) | 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 9) | 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 1021 a prime number?
Yes. 1021 is divisible only by 1 and itself.
What are the factors of 1021?
1, 1021.
What is 1021 in binary?
1111111101 (hexadecimal 3FD, octal 1775).
What is the square root of 1021?
About 31.9531.
What is 1021 in Roman numerals?
MXXI.
Is 1021 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 1021?
1021 is a twin prime (1019 and 1021 are both prime); the 172nd prime number.