3642
3642 is a even composite number that follows 3641 and precedes 3643. It is composed of 8 distinct factors: 1, 2, 3, 6, 607, 1214, 1821, 3642. Its prime factorization can be written as 2 × 3 × 607. 3642 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3642 is represented as 111000111010 in binary and E3A in hexadecimal. Historically, it is written as MMMDCXLII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 3 × 607) reveals 3 prime building blocks.
Divisible by 2
3642 ends in 2, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 42 are not divisible by 4.
Divisible by 5
3642 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 15 is not a multiple of 9.
Divisible by 10
3642 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 3642 within several notable number theory sequences:
Timeline
Deep dive
How 3642 breaks down
3642 carries 8 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 3654, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111000111010 supports bitwise reasoning, hexadecimal E3A aligns with computing notation, and the Roman numeral MMMDCXLII keeps the encyclopedic tradition alive. These attributes make 3642 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3642 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3637–3647) to tune search ranges, and educators feature 3642 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, Abundant numbers) help historians, numerologists, and trivia writers tie 3642 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 3642
Is 3642 a prime number?
3642 is composite with 8 total factors and the prime factorization 2 × 3 × 607.
What is the prime factorization of 3642?
It breaks down as 2 × 3 × 607, multiplying the primes 2 × 3 × 607.
How is 3642 represented in binary and hexadecimal?
3642 converts to 111000111010 in binary and E3A in hexadecimal, which are helpful for computer science applications.
Is 3642 a perfect square, cube, or triangular number?
3642 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3642?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.