724
724 is a even composite number that follows 723 and precedes 725. It is composed of 6 distinct factors: 1, 2, 4, 181, 362, 724. Its prime factorization can be written as 2^2 × 181. 724 is classified as a deficient number based on the sum of its proper divisors. In computer science, 724 is represented as 1011010100 in binary and 2D4 in hexadecimal. Historically, it is written as DCCXXIV in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (2^2 × 181) reveals 3 prime building blocks.
Divisible by 2
724 ends in 4, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 24 form a multiple of 4.
Divisible by 5
724 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 13 is not a multiple of 9.
Divisible by 10
724 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 724 within several notable number theory sequences:
Timeline
Deep dive
How 724 breaks down
724 carries 6 distinct factors and a digit signature of 13 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 550, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011010100 supports bitwise reasoning, hexadecimal 2D4 aligns with computing notation, and the Roman numeral DCCXXIV keeps the encyclopedic tradition alive. These attributes make 724 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 724 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (719–729) to tune search ranges, and educators feature 724 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, Deficient numbers) help historians, numerologists, and trivia writers tie 724 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 724
Is 724 a prime number?
724 is composite with 6 total factors and the prime factorization 2^2 × 181.
What is the prime factorization of 724?
It breaks down as 2^2 × 181, multiplying the primes 2 × 2 × 181.
How is 724 represented in binary and hexadecimal?
724 converts to 1011010100 in binary and 2D4 in hexadecimal, which are helpful for computer science applications.
Is 724 a perfect square, cube, or triangular number?
724 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 724?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.