1744
1744 is a even composite number that follows 1743 and precedes 1745. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 109, 218, 436, 872, 1744. Its prime factorization can be written as 2^4 × 109. 1744 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1744 is represented as 11011010000 in binary and 6D0 in hexadecimal. Historically, it is written as MDCCXLIV in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 109) reveals 5 prime building blocks.
Divisible by 2
1744 ends in 4, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 44 form a multiple of 4.
Divisible by 5
1744 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 16 is not a multiple of 9.
Divisible by 10
1744 does not end in 0.
Divisible by 11
The alternating digit sum -6 is not a multiple of 11.
Deficient classification and digit analytics place 1744 within several notable number theory sequences:
Timeline
Deep dive
How 1744 breaks down
1744 carries 10 distinct factors and a digit signature of 16 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 1666, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11011010000 supports bitwise reasoning, hexadecimal 6D0 aligns with computing notation, and the Roman numeral MDCCXLIV keeps the encyclopedic tradition alive. These attributes make 1744 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1744 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1739–1749) to tune search ranges, and educators feature 1744 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 1744 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 1744
Is 1744 a prime number?
1744 is composite with 10 total factors and the prime factorization 2^4 × 109.
What is the prime factorization of 1744?
It breaks down as 2^4 × 109, multiplying the primes 2 × 2 × 2 × 2 × 109.
How is 1744 represented in binary and hexadecimal?
1744 converts to 11011010000 in binary and 6D0 in hexadecimal, which are helpful for computer science applications.
Is 1744 a perfect square, cube, or triangular number?
1744 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1744?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.