3728
3728 is a even composite number that follows 3727 and precedes 3729. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 233, 466, 932, 1864, 3728. Its prime factorization can be written as 2^4 × 233. 3728 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3728 is represented as 111010010000 in binary and E90 in hexadecimal. Historically, it is written as MMMDCCXXVIII in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 233) reveals 5 prime building blocks.
Divisible by 2
3728 ends in 8, so it is even.
Divisible by 3
The digit sum 20 is not a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
3728 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 20 is not a multiple of 9.
Divisible by 10
3728 does not end in 0.
Divisible by 11
The alternating digit sum -10 is not a multiple of 11.
Deficient classification and digit analytics place 3728 within several notable number theory sequences:
Timeline
Deep dive
How 3728 breaks down
3728 carries 10 distinct factors and a digit signature of 20 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 3526, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111010010000 supports bitwise reasoning, hexadecimal E90 aligns with computing notation, and the Roman numeral MMMDCCXXVIII keeps the encyclopedic tradition alive. These attributes make 3728 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3728 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3723–3733) to tune search ranges, and educators feature 3728 in worksheets about factor trees. Its binary footprint of length 12 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 3728 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 3728
Is 3728 a prime number?
3728 is composite with 10 total factors and the prime factorization 2^4 × 233.
What is the prime factorization of 3728?
It breaks down as 2^4 × 233, multiplying the primes 2 × 2 × 2 × 2 × 233.
How is 3728 represented in binary and hexadecimal?
3728 converts to 111010010000 in binary and E90 in hexadecimal, which are helpful for computer science applications.
Is 3728 a perfect square, cube, or triangular number?
3728 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3728?
The digits sum to 20, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.