1864
1864 is a even composite number that follows 1863 and precedes 1865. It is composed of 8 distinct factors: 1, 2, 4, 8, 233, 466, 932, 1864. Its prime factorization can be written as 2^3 × 233. 1864 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1864 is represented as 11101001000 in binary and 748 in hexadecimal. Historically, it is written as MDCCCLXIV in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2^3 × 233) reveals 4 prime building blocks.
Divisible by 2
1864 ends in 4, so it is even.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
1864 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 19 is not a multiple of 9.
Divisible by 10
1864 does not end in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Deficient classification and digit analytics place 1864 within several notable number theory sequences:
Timeline
Deep dive
How 1864 breaks down
1864 carries 8 distinct factors and a digit signature of 19 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 1646, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11101001000 supports bitwise reasoning, hexadecimal 748 aligns with computing notation, and the Roman numeral MDCCCLXIV keeps the encyclopedic tradition alive. These attributes make 1864 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1864 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1859–1869) to tune search ranges, and educators feature 1864 in worksheets about factor trees. Its binary footprint of length 11 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 1864 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 1864
Is 1864 a prime number?
1864 is composite with 8 total factors and the prime factorization 2^3 × 233.
What is the prime factorization of 1864?
It breaks down as 2^3 × 233, multiplying the primes 2 × 2 × 2 × 233.
How is 1864 represented in binary and hexadecimal?
1864 converts to 11101001000 in binary and 748 in hexadecimal, which are helpful for computer science applications.
Is 1864 a perfect square, cube, or triangular number?
1864 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1864?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.