1600
1600 is a even composite number that follows 1599 and precedes 1601. It is composed of 21 distinct factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600. Its prime factorization can be written as 2^6 × 5^2. 1600 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1600 is represented as 11001000000 in binary and 640 in hexadecimal. Historically, it is written as MDC in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
21 FactorsProperties
The prime factorization (2^6 × 5^2) reveals 8 prime building blocks.
Divisible by 2
1600 ends in 0, so it is even.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
1600 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 7 is not a multiple of 9.
Divisible by 10
1600 ends in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Abundant classification and digit analytics place 1600 within several notable number theory sequences:
Timeline
Deep dive
How 1600 breaks down
1600 carries 21 distinct factors and a digit signature of 7 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 2337, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11001000000 supports bitwise reasoning, hexadecimal 640 aligns with computing notation, and the Roman numeral MDC keeps the encyclopedic tradition alive. These attributes make 1600 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1600 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1595–1605) to tune search ranges, and educators feature 1600 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, Perfect squares) help historians, numerologists, and trivia writers tie 1600 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 1600
Is 1600 a prime number?
1600 is composite with 21 total factors and the prime factorization 2^6 × 5^2.
What is the prime factorization of 1600?
It breaks down as 2^6 × 5^2, multiplying the primes 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5.
How is 1600 represented in binary and hexadecimal?
1600 converts to 11001000000 in binary and 640 in hexadecimal, which are helpful for computer science applications.
Is 1600 a perfect square, cube, or triangular number?
1600 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1600?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.