The number 1012
1012 is a composite number with 12 divisors. Its prime factorisation is × 11 × 23. Divisors (12): 1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506, 1012.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1012: a Harshad number: divisible by its digit sum 4.
- 2
1012 is composite. Its prime factorisation is
- 3
The divisors add up to 2016; without 1012 itself that is 1004, so 1012 is deficient (1004 is less than 1012). Euler's totient φ(1012) = 440 numbers up to 1012 share no factor with it.
- 4
The digits of 1012 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 111 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1012 = 2^{2} \times 11 \times 23 \]1012 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 2016 |
| Euler totient φ(n) | 440 |
| Square | 1024144 |
| Cube | 1036433728 |
| Square root | 31.811947 (= 2√253) |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 111 |
| Scientific notation | 1.012 × |
1012 in other forms
| Form | Value |
|---|---|
| In words | one thousand and twelve |
| Roman numerals | MXII |
| Binary (base 2) | 1111110100 |
| Octal (base 8) | 1764 |
| Hexadecimal (base 16) | 3F4 |
| Base 3 | 1101111 |
| As time | 1012 seconds = 16 min 52 s |
Is 1012 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1012 ÷ 2 = 506) | 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 | Yes (1012 ÷ 4 = 253) | 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 | No (remainder 4) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 (1012 ÷ 11 = 92) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1012 a prime number?
No. 1012 = × 11 × 23, so it is divisible by 2.
What are the factors of 1012?
1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506, 1012.
What is 1012 in binary?
1111110100 (hexadecimal 3F4, octal 1764).
What is the square root of 1012?
About 31.8119, exactly 2√253.
What is 1012 in Roman numerals?
MXII.
Is 1012 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 1012?
1012 is a Harshad number: divisible by its digit sum 4.