1938
1938 is a even composite number that follows 1937 and precedes 1939. It is composed of 16 distinct factors: 1, 2, 3, 6, 17, 19, 34, 38, 51, 57, 102, 114, 323, 646, 969, 1938. Its prime factorization can be written as 2 × 3 × 17 × 19. 1938 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1938 is represented as 11110010010 in binary and 792 in hexadecimal. Historically, it is written as MCMXXXVIII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2 × 3 × 17 × 19) reveals 4 prime building blocks.
Divisible by 2
1938 ends in 8, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 38 are not divisible by 4.
Divisible by 5
1938 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 21 is not a multiple of 9.
Divisible by 10
1938 does not end in 0.
Divisible by 11
The alternating digit sum -13 is not a multiple of 11.
Abundant classification and digit analytics place 1938 within several notable number theory sequences:
Timeline
Deep dive
How 1938 breaks down
1938 carries 16 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 2382, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11110010010 supports bitwise reasoning, hexadecimal 792 aligns with computing notation, and the Roman numeral MCMXXXVIII keeps the encyclopedic tradition alive. These attributes make 1938 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1938 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1933–1943) to tune search ranges, and educators feature 1938 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 1938 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 1938
Is 1938 a prime number?
1938 is composite with 16 total factors and the prime factorization 2 × 3 × 17 × 19.
What is the prime factorization of 1938?
It breaks down as 2 × 3 × 17 × 19, multiplying the primes 2 × 3 × 17 × 19.
How is 1938 represented in binary and hexadecimal?
1938 converts to 11110010010 in binary and 792 in hexadecimal, which are helpful for computer science applications.
Is 1938 a perfect square, cube, or triangular number?
1938 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1938?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.