The number 1122
1122 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 11 × 17. Divisors (16): 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1122: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 6.
- 2
1122 is composite. Its prime factorisation is
- 3
The divisors add up to 2592; without 1122 itself that is 1470, so 1122 is abundant (1470 is more than 1122). Euler's totient φ(1122) = 320 numbers up to 1122 share no factor with it.
- 4
The digits of 1122 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1122 = 2 \times 3 \times 11 \times 17 \]
1122 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 2592 |
| Euler totient φ(n) | 320 |
| Square | 1258884 |
| Cube | 1412467848 |
| Square root | 33.496268 |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 44 |
| Scientific notation | 1.122 × |
1122 in other forms
| Form | Value |
|---|---|
| In words | one thousand one hundred and twenty-two |
| Roman numerals | MCXXII |
| Binary (base 2) | 10001100010 |
| Octal (base 8) | 2142 |
| Hexadecimal (base 16) | 462 |
| Base 3 | 1112120 |
| As time | 1122 seconds = 18 min 42 s |
Is 1122 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1122 ÷ 2 = 561) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1122 ÷ 3 = 374) | 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 | Yes (1122 ÷ 6 = 187) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | 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 | Yes (1122 ÷ 11 = 102) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1122 a prime number?
No. 1122 = 2 × 3 × 11 × 17, so it is divisible by 2.
What are the factors of 1122?
1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122.
What is 1122 in binary?
10001100010 (hexadecimal 462, octal 2142).
What is the square root of 1122?
About 33.4963.
What is 1122 in Roman numerals?
MCXXII.
Is 1122 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 1122?
1122 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 6.