The number 1022
1022 is a composite number with 8 divisors. Its prime factorisation is 2 × 7 × 73. Divisors (8): 1, 2, 7, 14, 73, 146, 511, 1022.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1022 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1022 is composite. Its prime factorisation is
- 3
The divisors add up to 1776; without 1022 itself that is 754, so 1022 is deficient (754 is less than 1022). Euler's totient φ(1022) = 432 numbers up to 1022 share no factor with it.
- 4
The digits of 1022 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1022 = 2 \times 7 \times 73 \]
1022 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1776 |
| Euler totient φ(n) | 432 |
| Square | 1044484 |
| Cube | 1067462648 |
| Square root | 31.968735 |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 62 |
| Scientific notation | 1.022 × |
1022 in other forms
| Form | Value |
|---|---|
| In words | one thousand and twenty-two |
| Roman numerals | MXXII |
| Binary (base 2) | 1111111110 |
| Octal (base 8) | 1776 |
| Hexadecimal (base 16) | 3FE |
| Base 3 | 1101212 |
| As time | 1022 seconds = 17 min 2 s |
Is 1022 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1022 ÷ 2 = 511) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | 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 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1022 ÷ 7 = 146) | 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 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 2) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1022 a prime number?
No. 1022 = 2 × 7 × 73, so it is divisible by 2.
What are the factors of 1022?
1, 2, 7, 14, 73, 146, 511, 1022.
What is 1022 in binary?
1111111110 (hexadecimal 3FE, octal 1776).
What is the square root of 1022?
About 31.9687.
What is 1022 in Roman numerals?
MXXII.
Is 1022 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 1022?
It is a composite number with 8 divisors.