744
744 is a even composite number that follows 743 and precedes 745. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744. Its prime factorization can be written as 2^3 × 3 × 31. 744 is classified as a abundant number based on the sum of its proper divisors. In computer science, 744 is represented as 1011101000 in binary and 2E8 in hexadecimal. Historically, it is written as DCCXLIV in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 31) reveals 5 prime building blocks.
Divisible by 2
744 ends in 4, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 44 form a multiple of 4.
Divisible by 5
744 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 15 is not a multiple of 9.
Divisible by 10
744 does not end in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Abundant classification and digit analytics place 744 within several notable number theory sequences:
Timeline
Deep dive
How 744 breaks down
744 carries 16 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 1176, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011101000 supports bitwise reasoning, hexadecimal 2E8 aligns with computing notation, and the Roman numeral DCCXLIV keeps the encyclopedic tradition alive. These attributes make 744 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 744 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (739–749) to tune search ranges, and educators feature 744 in worksheets about factor trees. Its binary footprint of length 10 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Abundant numbers) help historians, numerologists, and trivia writers tie 744 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 744
Is 744 a prime number?
744 is composite with 16 total factors and the prime factorization 2^3 × 3 × 31.
What is the prime factorization of 744?
It breaks down as 2^3 × 3 × 31, multiplying the primes 2 × 2 × 2 × 3 × 31.
How is 744 represented in binary and hexadecimal?
744 converts to 1011101000 in binary and 2E8 in hexadecimal, which are helpful for computer science applications.
Is 744 a perfect square, cube, or triangular number?
744 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 744?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.