3456
3456 is a even composite number that follows 3455 and precedes 3457. It is composed of 32 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 288, 384, 432, 576, 864, 1152, 1728, 3456. Its prime factorization can be written as 2^7 × 3^3. 3456 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3456 is represented as 110110000000 in binary and D80 in hexadecimal. Historically, it is written as MMMCDLVI in Roman numerals.
Factor Analysis
32 FactorsProperties
The prime factorization (2^7 × 3^3) reveals 10 prime building blocks.
Divisible by 2
3456 ends in 6, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 56 form a multiple of 4.
Divisible by 5
3456 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 18 is a multiple of 9.
Divisible by 10
3456 does not end in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Abundant classification and digit analytics place 3456 within several notable number theory sequences:
Timeline
Deep dive
How 3456 breaks down
3456 carries 32 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 6744, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110110000000 supports bitwise reasoning, hexadecimal D80 aligns with computing notation, and the Roman numeral MMMCDLVI keeps the encyclopedic tradition alive. These attributes make 3456 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3456 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3451–3461) to tune search ranges, and educators feature 3456 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 3456 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 3456
Is 3456 a prime number?
3456 is composite with 32 total factors and the prime factorization 2^7 × 3^3.
What is the prime factorization of 3456?
It breaks down as 2^7 × 3^3, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3.
How is 3456 represented in binary and hexadecimal?
3456 converts to 110110000000 in binary and D80 in hexadecimal, which are helpful for computer science applications.
Is 3456 a perfect square, cube, or triangular number?
3456 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3456?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.