3688
3688 is a even composite number that follows 3687 and precedes 3689. It is composed of 8 distinct factors: 1, 2, 4, 8, 461, 922, 1844, 3688. Its prime factorization can be written as 2^3 × 461. 3688 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3688 is represented as 111001101000 in binary and E68 in hexadecimal. Historically, it is written as MMMDCLXXXVIII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2^3 × 461) reveals 4 prime building blocks.
Divisible by 2
3688 ends in 8, so it is even.
Divisible by 3
The digit sum 25 is not a multiple of 3.
Divisible by 4
The last two digits 88 form a multiple of 4.
Divisible by 5
3688 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 25 is not a multiple of 9.
Divisible by 10
3688 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Deficient classification and digit analytics place 3688 within several notable number theory sequences:
Timeline
Deep dive
How 3688 breaks down
3688 carries 8 distinct factors and a digit signature of 25 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 3242, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111001101000 supports bitwise reasoning, hexadecimal E68 aligns with computing notation, and the Roman numeral MMMDCLXXXVIII keeps the encyclopedic tradition alive. These attributes make 3688 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3688 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3683–3693) to tune search ranges, and educators feature 3688 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 3688 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 3688
Is 3688 a prime number?
3688 is composite with 8 total factors and the prime factorization 2^3 × 461.
What is the prime factorization of 3688?
It breaks down as 2^3 × 461, multiplying the primes 2 × 2 × 2 × 461.
How is 3688 represented in binary and hexadecimal?
3688 converts to 111001101000 in binary and E68 in hexadecimal, which are helpful for computer science applications.
Is 3688 a perfect square, cube, or triangular number?
3688 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3688?
The digits sum to 25, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.