1596
1596 is a even composite number that follows 1595 and precedes 1597. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 7, 12, 14, 19, 21, 28, 38, 42, 57, 76, 84, 114, 133, 228, 266, 399, 532, 798, 1596. Its prime factorization can be written as 2^2 × 3 × 7 × 19. 1596 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1596 is represented as 11000111100 in binary and 63C in hexadecimal. Historically, it is written as MDXCVI in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 3 × 7 × 19) reveals 5 prime building blocks.
Divisible by 2
1596 ends in 6, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 96 form a multiple of 4.
Divisible by 5
1596 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 21 is not a multiple of 9.
Divisible by 10
1596 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 1596 within several notable number theory sequences:
Timeline
Deep dive
How 1596 breaks down
1596 carries 24 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 2884, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11000111100 supports bitwise reasoning, hexadecimal 63C aligns with computing notation, and the Roman numeral MDXCVI keeps the encyclopedic tradition alive. These attributes make 1596 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1596 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1591–1601) to tune search ranges, and educators feature 1596 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, Abundant numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 1596 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 1596
Is 1596 a prime number?
1596 is composite with 24 total factors and the prime factorization 2^2 × 3 × 7 × 19.
What is the prime factorization of 1596?
It breaks down as 2^2 × 3 × 7 × 19, multiplying the primes 2 × 2 × 3 × 7 × 19.
How is 1596 represented in binary and hexadecimal?
1596 converts to 11000111100 in binary and 63C in hexadecimal, which are helpful for computer science applications.
Is 1596 a perfect square, cube, or triangular number?
1596 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 1596?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.