The number 1026
1026 is a composite number with 16 divisors. Its prime factorisation is 2 × × 19. Divisors (16): 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 114, 171, 342, 513, 1026.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1026: a Harshad number: divisible by its digit sum 9.
- 2
1026 is composite. Its prime factorisation is
- 3
The divisors add up to 2400; without 1026 itself that is 1374, so 1026 is abundant (1374 is more than 1026). Euler's totient φ(1026) = 324 numbers up to 1026 share no factor with it.
- 4
The digits of 1026 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 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1026 = 2 \times 3^{3} \times 19 \]1026 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 2400 |
| Euler totient φ(n) | 324 |
| Square | 1052676 |
| Cube | 1080045576 |
| Square root | 32.031235 (= 3√114) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 36 |
| Scientific notation | 1.026 × |
1026 in other forms
| Form | Value |
|---|---|
| In words | one thousand and twenty-six |
| Roman numerals | MXXVI |
| Binary (base 2) | 10000000010 |
| Octal (base 8) | 2002 |
| Hexadecimal (base 16) | 402 |
| Base 3 | 1102000 |
| As time | 1026 seconds = 17 min 6 s |
Is 1026 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1026 ÷ 2 = 513) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1026 ÷ 3 = 342) | 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 | Yes (1026 ÷ 6 = 171) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1026 ÷ 9 = 114) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1026 a prime number?
No. 1026 = 2 × × 19, so it is divisible by 2.
What are the factors of 1026?
1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 114, 171, 342, 513, 1026.
What is 1026 in binary?
10000000010 (hexadecimal 402, octal 2002).
What is the square root of 1026?
About 32.0312, exactly 3√114.
What is 1026 in Roman numerals?
MXXVI.
Is 1026 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1026?
1026 is a Harshad number: divisible by its digit sum 9.