3744
3744 is a even composite number that follows 3743 and precedes 3745. It is composed of 36 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 72, 78, 96, 104, 117, 144, 156, 208, 234, 288, 312, 416, 468, 624, 936, 1248, 1872, 3744. Its prime factorization can be written as 2^5 × 3^2 × 13. 3744 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3744 is represented as 111010100000 in binary and EA0 in hexadecimal. Historically, it is written as MMMDCCXLIV in Roman numerals.
Factor Analysis
36 FactorsProperties
The prime factorization (2^5 × 3^2 × 13) reveals 8 prime building blocks.
Divisible by 2
3744 ends in 4, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 44 form a multiple of 4.
Divisible by 5
3744 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 18 is a multiple of 9.
Divisible by 10
3744 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 3744 within several notable number theory sequences:
Timeline
Deep dive
How 3744 breaks down
3744 carries 36 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 7722, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111010100000 supports bitwise reasoning, hexadecimal EA0 aligns with computing notation, and the Roman numeral MMMDCCXLIV keeps the encyclopedic tradition alive. These attributes make 3744 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3744 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3739–3749) to tune search ranges, and educators feature 3744 in worksheets about factor trees. Its binary footprint of length 12 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 3744 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 3744
Is 3744 a prime number?
3744 is composite with 36 total factors and the prime factorization 2^5 × 3^2 × 13.
What is the prime factorization of 3744?
It breaks down as 2^5 × 3^2 × 13, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 3 × 13.
How is 3744 represented in binary and hexadecimal?
3744 converts to 111010100000 in binary and EA0 in hexadecimal, which are helpful for computer science applications.
Is 3744 a perfect square, cube, or triangular number?
3744 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3744?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.