3136
3136 is a even composite number that follows 3135 and precedes 3137. It is composed of 21 distinct factors: 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136. Its prime factorization can be written as 2^6 × 7^2. 3136 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3136 is represented as 110001000000 in binary and C40 in hexadecimal. Historically, it is written as MMMCXXXVI in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
21 FactorsProperties
The prime factorization (2^6 × 7^2) reveals 8 prime building blocks.
Divisible by 2
3136 ends in 6, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 36 form a multiple of 4.
Divisible by 5
3136 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 13 is not a multiple of 9.
Divisible by 10
3136 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 3136 within several notable number theory sequences:
Timeline
Deep dive
How 3136 breaks down
3136 carries 21 distinct factors and a digit signature of 13 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 4103, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110001000000 supports bitwise reasoning, hexadecimal C40 aligns with computing notation, and the Roman numeral MMMCXXXVI keeps the encyclopedic tradition alive. These attributes make 3136 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3136 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3131–3141) to tune search ranges, and educators feature 3136 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, Perfect squares) help historians, numerologists, and trivia writers tie 3136 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 3136
Is 3136 a prime number?
3136 is composite with 21 total factors and the prime factorization 2^6 × 7^2.
What is the prime factorization of 3136?
It breaks down as 2^6 × 7^2, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7.
How is 3136 represented in binary and hexadecimal?
3136 converts to 110001000000 in binary and C40 in hexadecimal, which are helpful for computer science applications.
Is 3136 a perfect square, cube, or triangular number?
3136 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3136?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.