The number 1100
1100 is a composite number with 18 divisors. Its prime factorisation is × × 11. Divisors (18): 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275 … 1100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1100: a Harshad number: divisible by its digit sum 2.
- 2
1100 is composite. Its prime factorisation is
- 3
The divisors add up to 2604; without 1100 itself that is 1504, so 1100 is abundant (1504 is more than 1100). Euler's totient φ(1100) = 400 numbers up to 1100 share no factor with it.
- 4
The digits of 1100 add up to 2, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 93 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1100 = 2^{2} \times 5^{2} \times 11 \]1100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 2604 |
| Euler totient φ(n) | 400 |
| Square | 1210000 |
| Cube | 1331000000 |
| Square root | 33.166248 (= 10√11) |
| Digit sum / digital root | 2 / 2 |
| Collatz steps to 1 | 93 |
| Scientific notation | 1.1 × |
1100 in other forms
| Form | Value |
|---|---|
| In words | one thousand one hundred |
| Roman numerals | MC |
| Binary (base 2) | 10001001100 |
| Octal (base 8) | 2114 |
| Hexadecimal (base 16) | 44C |
| Base 3 | 1111202 |
| As time | 1100 seconds = 18 min 20 s |
Is 1100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1100 ÷ 2 = 550) | 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 | Yes (1100 ÷ 4 = 275) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1100 ÷ 5 = 220) | 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 | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1100 ÷ 10 = 110) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (1100 ÷ 11 = 100) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1100 a prime number?
No. 1100 = × × 11, so it is divisible by 2.
What are the factors of 1100?
1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550, 1100.
What is 1100 in binary?
10001001100 (hexadecimal 44C, octal 2114).
What is the square root of 1100?
About 33.1662, exactly 10√11.
What is 1100 in Roman numerals?
MC.
Is 1100 divisible by 3?
No. Its digits add up to 2, which is not a multiple of 3.
What is special about the number 1100?
1100 is a Harshad number: divisible by its digit sum 2.