The number 1152
1152 is a composite number with 24 divisors. Its prime factorisation is × . Divisors (24): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 1152.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1152: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
1152 is composite. Its prime factorisation is
- 3
The divisors add up to 3315; without 1152 itself that is 2163, so 1152 is abundant (2163 is more than 1152). Euler's totient φ(1152) = 384 numbers up to 1152 share no factor with it.
- 4
The digits of 1152 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 26 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1152 = 2^{7} \times 3^{2} \]1152 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 3315 |
| Euler totient φ(n) | 384 |
| Square | 1327104 |
| Cube | 1528823808 |
| Square root | 33.941125 (= 24√2) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 26 |
| Scientific notation | 1.152 × |
1152 in other forms
| Form | Value |
|---|---|
| In words | one thousand one hundred and fifty-two |
| Roman numerals | MCLII |
| Binary (base 2) | 10010000000 |
| Octal (base 8) | 2200 |
| Hexadecimal (base 16) | 480 |
| Base 3 | 1120200 |
| As time | 1152 seconds = 19 min 12 s |
Is 1152 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1152 ÷ 2 = 576) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1152 ÷ 3 = 384) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1152 ÷ 4 = 288) | 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 (1152 ÷ 6 = 192) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 | Yes (1152 ÷ 8 = 144) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1152 ÷ 9 = 128) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1152 ÷ 12 = 96) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1152 a prime number?
No. 1152 = × , so it is divisible by 2.
What are the factors of 1152?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152.
What is 1152 in binary?
10010000000 (hexadecimal 480, octal 2200).
What is the square root of 1152?
About 33.9411, exactly 24√2.
What is 1152 in Roman numerals?
MCLII.
Is 1152 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1152?
1152 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.