The number 1056
1056 is a composite number with 24 divisors. Its prime factorisation is × 3 × 11. Divisors (24): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66 … 1056.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1056: a Harshad number: divisible by its digit sum 12.
- 2
1056 is composite. Its prime factorisation is
- 3
The divisors add up to 3024; without 1056 itself that is 1968, so 1056 is abundant (1968 is more than 1056). Euler's totient φ(1056) = 320 numbers up to 1056 share no factor with it.
- 4
The digits of 1056 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 31 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1056 = 2^{5} \times 3 \times 11 \]1056 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 3024 |
| Euler totient φ(n) | 320 |
| Square | 1115136 |
| Cube | 1177583616 |
| Square root | 32.496154 (= 4√66) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 31 |
| Scientific notation | 1.056 × |
1056 in other forms
| Form | Value |
|---|---|
| In words | one thousand and fifty-six |
| Roman numerals | MLVI |
| Binary (base 2) | 10000100000 |
| Octal (base 8) | 2040 |
| Hexadecimal (base 16) | 420 |
| Base 3 | 1110010 |
| As time | 1056 seconds = 17 min 36 s |
Is 1056 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1056 ÷ 2 = 528) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1056 ÷ 3 = 352) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1056 ÷ 4 = 264) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1056 ÷ 6 = 176) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (1056 ÷ 8 = 132) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (1056 ÷ 11 = 96) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1056 ÷ 12 = 88) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1056 a prime number?
No. 1056 = × 3 × 11, so it is divisible by 2.
What are the factors of 1056?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 88, 96, 132, 176, 264, 352, 528, 1056.
What is 1056 in binary?
10000100000 (hexadecimal 420, octal 2040).
What is the square root of 1056?
About 32.4962, exactly 4√66.
What is 1056 in Roman numerals?
MLVI.
Is 1056 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1056?
1056 is a Harshad number: divisible by its digit sum 12.