The number 1006
1006 is a composite number with 4 divisors. Its prime factorisation is 2 × 503. Divisors (4): 1, 2, 503, 1006.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1006: a semiprime: 2 × 503, the product of two primes.
- 2
1006 is composite. Its prime factorisation is
- 3
The divisors add up to 1512; without 1006 itself that is 506, so 1006 is deficient (506 is less than 1006). Euler's totient φ(1006) = 502 numbers up to 1006 share no factor with it.
- 4
The digits of 1006 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 67 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1006 = 2 \times 503 \]
1006 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 1512 |
| Euler totient φ(n) | 502 |
| Square | 1012036 |
| Cube | 1018108216 |
| Square root | 31.717503 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 67 |
| Scientific notation | 1.006 × |
1006 in other forms
| Form | Value |
|---|---|
| In words | one thousand and six |
| Roman numerals | MVI |
| Binary (base 2) | 1111101110 |
| Octal (base 8) | 1756 |
| Hexadecimal (base 16) | 3EE |
| Base 3 | 1101021 |
| As time | 1006 seconds = 16 min 46 s |
Is 1006 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1006 ÷ 2 = 503) | 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 | No (remainder 1) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | 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 | No (remainder 5) | 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 1006 a prime number?
No. 1006 = 2 × 503, so it is divisible by 2.
What are the factors of 1006?
1, 2, 503, 1006.
What is 1006 in binary?
1111101110 (hexadecimal 3EE, octal 1756).
What is the square root of 1006?
About 31.7175.
What is 1006 in Roman numerals?
MVI.
Is 1006 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 1006?
1006 is a semiprime: 2 × 503, the product of two primes.