1802
1802 is a even composite number that follows 1801 and precedes 1803. It is composed of 8 distinct factors: 1, 2, 17, 34, 53, 106, 901, 1802. Its prime factorization can be written as 2 × 17 × 53. 1802 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1802 is represented as 11100001010 in binary and 70A in hexadecimal. Historically, it is written as MDCCCII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 17 × 53) reveals 3 prime building blocks.
Divisible by 2
1802 ends in 2, so it is even.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 02 are not divisible by 4.
Divisible by 5
1802 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 11 is not a multiple of 9.
Divisible by 10
1802 does not end in 0.
Divisible by 11
The alternating digit sum -9 is not a multiple of 11.
Deficient classification and digit analytics place 1802 within several notable number theory sequences:
Timeline
Deep dive
How 1802 breaks down
1802 carries 8 distinct factors and a digit signature of 11 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 1114, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11100001010 supports bitwise reasoning, hexadecimal 70A aligns with computing notation, and the Roman numeral MDCCCII keeps the encyclopedic tradition alive. These attributes make 1802 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1802 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1797–1807) to tune search ranges, and educators feature 1802 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 1802 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 1802
Is 1802 a prime number?
1802 is composite with 8 total factors and the prime factorization 2 × 17 × 53.
What is the prime factorization of 1802?
It breaks down as 2 × 17 × 53, multiplying the primes 2 × 17 × 53.
How is 1802 represented in binary and hexadecimal?
1802 converts to 11100001010 in binary and 70A in hexadecimal, which are helpful for computer science applications.
Is 1802 a perfect square, cube, or triangular number?
1802 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1802?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.