3696
3696 is a even composite number that follows 3695 and precedes 3697. It is composed of 40 distinct factors: 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 33, 42, 44, 48, 56, 66, 77, 84, 88, 112, 132, 154, 168, 176, 231, 264, 308, 336, 462, 528, 616, 924, 1232, 1848, 3696. Its prime factorization can be written as 2^4 × 3 × 7 × 11. 3696 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3696 is represented as 111001110000 in binary and E70 in hexadecimal. Historically, it is written as MMMDCXCVI in Roman numerals.
Factor Analysis
40 FactorsProperties
The prime factorization (2^4 × 3 × 7 × 11) reveals 7 prime building blocks.
Divisible by 2
3696 ends in 6, so it is even.
Divisible by 3
The digit sum 24 is a multiple of 3.
Divisible by 4
The last two digits 96 form a multiple of 4.
Divisible by 5
3696 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 24 is not a multiple of 9.
Divisible by 10
3696 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 3696 within several notable number theory sequences:
Timeline
Deep dive
How 3696 breaks down
3696 carries 40 distinct factors and a digit signature of 24 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 8208, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111001110000 supports bitwise reasoning, hexadecimal E70 aligns with computing notation, and the Roman numeral MMMDCXCVI keeps the encyclopedic tradition alive. These attributes make 3696 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3696 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3691–3701) to tune search ranges, and educators feature 3696 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 3696 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 3696
Is 3696 a prime number?
3696 is composite with 40 total factors and the prime factorization 2^4 × 3 × 7 × 11.
What is the prime factorization of 3696?
It breaks down as 2^4 × 3 × 7 × 11, multiplying the primes 2 × 2 × 2 × 2 × 3 × 7 × 11.
How is 3696 represented in binary and hexadecimal?
3696 converts to 111001110000 in binary and E70 in hexadecimal, which are helpful for computer science applications.
Is 3696 a perfect square, cube, or triangular number?
3696 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3696?
The digits sum to 24, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.