726
726 is a even composite number that follows 725 and precedes 727. It is composed of 12 distinct factors: 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726. Its prime factorization can be written as 2 × 3 × 11^2. 726 is classified as a abundant number based on the sum of its proper divisors. In computer science, 726 is represented as 1011010110 in binary and 2D6 in hexadecimal. Historically, it is written as DCCXXVI in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 3 × 11^2) reveals 4 prime building blocks.
Divisible by 2
726 ends in 6, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 26 are not divisible by 4.
Divisible by 5
726 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
726 does not end in 0.
Divisible by 11
The alternating digit sum 11 is a multiple of 11.
Abundant classification and digit analytics place 726 within several notable number theory sequences:
Timeline
Deep dive
How 726 breaks down
726 carries 12 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 870, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011010110 supports bitwise reasoning, hexadecimal 2D6 aligns with computing notation, and the Roman numeral DCCXXVI keeps the encyclopedic tradition alive. These attributes make 726 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 726 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (721–731) to tune search ranges, and educators feature 726 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 726 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 726
Is 726 a prime number?
726 is composite with 12 total factors and the prime factorization 2 × 3 × 11^2.
What is the prime factorization of 726?
It breaks down as 2 × 3 × 11^2, multiplying the primes 2 × 3 × 11 × 11.
How is 726 represented in binary and hexadecimal?
726 converts to 1011010110 in binary and 2D6 in hexadecimal, which are helpful for computer science applications.
Is 726 a perfect square, cube, or triangular number?
726 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 726?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.