The number 1038
1038 is a composite number with 8 divisors. Its prime factorisation is 2 × 3 × 173. Divisors (8): 1, 2, 3, 6, 173, 346, 519, 1038.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1038 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1038 is composite. Its prime factorisation is
- 3
The divisors add up to 2088; without 1038 itself that is 1050, so 1038 is abundant (1050 is more than 1038). Euler's totient φ(1038) = 344 numbers up to 1038 share no factor with it.
- 4
The digits of 1038 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 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1038 = 2 \times 3 \times 173 \]
1038 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 2088 |
| Euler totient φ(n) | 344 |
| Square | 1077444 |
| Cube | 1118386872 |
| Square root | 32.218007 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 62 |
| Scientific notation | 1.038 × |
1038 in other forms
| Form | Value |
|---|---|
| In words | one thousand and thirty-eight |
| Roman numerals | MXXXVIII |
| Binary (base 2) | 10000001110 |
| Octal (base 8) | 2016 |
| Hexadecimal (base 16) | 40E |
| Base 3 | 1102110 |
| As time | 1038 seconds = 17 min 18 s |
Is 1038 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1038 ÷ 2 = 519) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1038 ÷ 3 = 346) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1038 ÷ 6 = 173) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1038 a prime number?
No. 1038 = 2 × 3 × 173, so it is divisible by 2.
What are the factors of 1038?
1, 2, 3, 6, 173, 346, 519, 1038.
What is 1038 in binary?
10000001110 (hexadecimal 40E, octal 2016).
What is the square root of 1038?
About 32.2180.
What is 1038 in Roman numerals?
MXXXVIII.
Is 1038 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1038?
It is a composite number with 8 divisors.