The number 1016
1016 is a composite number with 8 divisors. Its prime factorisation is × 127. Divisors (8): 1, 2, 4, 8, 127, 254, 508, 1016.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1016: a Harshad number: divisible by its digit sum 8.
- 2
1016 is composite. Its prime factorisation is
- 3
The divisors add up to 1920; without 1016 itself that is 904, so 1016 is deficient (904 is less than 1016). Euler's totient φ(1016) = 504 numbers up to 1016 share no factor with it.
- 4
The digits of 1016 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1016 = 2^{3} \times 127 \]1016 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1920 |
| Euler totient φ(n) | 504 |
| Square | 1032256 |
| Cube | 1048772096 |
| Square root | 31.874755 (= 2√254) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 49 |
| Scientific notation | 1.016 × |
1016 in other forms
| Form | Value |
|---|---|
| In words | one thousand and sixteen |
| Roman numerals | MXVI |
| Binary (base 2) | 1111111000 |
| Octal (base 8) | 1770 |
| Hexadecimal (base 16) | 3F8 |
| Base 3 | 1101122 |
| As time | 1016 seconds = 16 min 56 s |
Is 1016 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1016 ÷ 2 = 508) | 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 (1016 ÷ 4 = 254) | 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 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 | Yes (1016 ÷ 8 = 127) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 4) | 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 1016 a prime number?
No. 1016 = × 127, so it is divisible by 2.
What are the factors of 1016?
1, 2, 4, 8, 127, 254, 508, 1016.
What is 1016 in binary?
1111111000 (hexadecimal 3F8, octal 1770).
What is the square root of 1016?
About 31.8748, exactly 2√254.
What is 1016 in Roman numerals?
MXVI.
Is 1016 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 1016?
1016 is a Harshad number: divisible by its digit sum 8.