The number 1090
1090 is a composite number with 8 divisors. Its prime factorisation is 2 × 5 × 109. Divisors (8): 1, 2, 5, 10, 109, 218, 545, 1090.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1090: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
1090 is composite. Its prime factorisation is
- 3
The divisors add up to 1980; without 1090 itself that is 890, so 1090 is deficient (890 is less than 1090). Euler's totient φ(1090) = 432 numbers up to 1090 share no factor with it.
- 4
The digits of 1090 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1090 = 2 \times 5 \times 109 \]
1090 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1980 |
| Euler totient φ(n) | 432 |
| Square | 1188100 |
| Cube | 1295029000 |
| Square root | 33.015148 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 44 |
| Scientific notation | 1.09 × |
1090 in other forms
| Form | Value |
|---|---|
| In words | one thousand and ninety |
| Roman numerals | MXC |
| Binary (base 2) | 10001000010 |
| Octal (base 8) | 2102 |
| Hexadecimal (base 16) | 442 |
| Base 3 | 1111101 |
| As time | 1090 seconds = 18 min 10 s |
Is 1090 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1090 ÷ 2 = 545) | 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 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1090 ÷ 5 = 218) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1090 ÷ 10 = 109) | 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 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1090 a prime number?
No. 1090 = 2 × 5 × 109, so it is divisible by 2.
What are the factors of 1090?
1, 2, 5, 10, 109, 218, 545, 1090.
What is 1090 in binary?
10001000010 (hexadecimal 442, octal 2102).
What is the square root of 1090?
About 33.0151.
What is 1090 in Roman numerals?
MXC.
Is 1090 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 1090?
1090 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.