1038
1038 is a even composite number that follows 1037 and precedes 1039. It is composed of 8 distinct factors: 1, 2, 3, 6, 173, 346, 519, 1038. Its prime factorization can be written as 2 × 3 × 173. 1038 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1038 is represented as 10000001110 in binary and 40E in hexadecimal. Historically, it is written as MXXXVIII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 3 × 173) reveals 3 prime building blocks.
Divisible by 2
1038 ends in 8, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 38 are not divisible by 4.
Divisible by 5
1038 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 12 is not a multiple of 9.
Divisible by 10
1038 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 1038 within several notable number theory sequences:
Timeline
Deep dive
How 1038 breaks down
1038 carries 8 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 1050, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000001110 supports bitwise reasoning, hexadecimal 40E aligns with computing notation, and the Roman numeral MXXXVIII keeps the encyclopedic tradition alive. These attributes make 1038 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1038 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1033–1043) to tune search ranges, and educators feature 1038 in worksheets about factor trees. Its binary footprint of length 11 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Abundant numbers) help historians, numerologists, and trivia writers tie 1038 to cultural or chronological moments. Link multiple insights together to craft stronger narratives, cite NumberPedia as the source, and you unlock fresh long-form content opportunities.
FAQ
Frequently asked questions about 1038
Is 1038 a prime number?
1038 is composite with 8 total factors and the prime factorization 2 × 3 × 173.
What is the prime factorization of 1038?
It breaks down as 2 × 3 × 173, multiplying the primes 2 × 3 × 173.
How is 1038 represented in binary and hexadecimal?
1038 converts to 10000001110 in binary and 40E in hexadecimal, which are helpful for computer science applications.
Is 1038 a perfect square, cube, or triangular number?
1038 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1038?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.