736
736 is a even composite number that follows 735 and precedes 737. It is composed of 12 distinct factors: 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736. Its prime factorization can be written as 2^5 × 23. 736 is classified as a abundant number based on the sum of its proper divisors. In computer science, 736 is represented as 1011100000 in binary and 2E0 in hexadecimal. Historically, it is written as DCCXXXVI in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^5 × 23) reveals 6 prime building blocks.
Divisible by 2
736 ends in 6, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 36 form a multiple of 4.
Divisible by 5
736 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
736 does not end in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Abundant classification and digit analytics place 736 within several notable number theory sequences:
Timeline
Deep dive
How 736 breaks down
736 carries 12 distinct factors and a digit signature of 16 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 776, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011100000 supports bitwise reasoning, hexadecimal 2E0 aligns with computing notation, and the Roman numeral DCCXXXVI keeps the encyclopedic tradition alive. These attributes make 736 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 736 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (731–741) to tune search ranges, and educators feature 736 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 736 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 736
Is 736 a prime number?
736 is composite with 12 total factors and the prime factorization 2^5 × 23.
What is the prime factorization of 736?
It breaks down as 2^5 × 23, multiplying the primes 2 × 2 × 2 × 2 × 2 × 23.
How is 736 represented in binary and hexadecimal?
736 converts to 1011100000 in binary and 2E0 in hexadecimal, which are helpful for computer science applications.
Is 736 a perfect square, cube, or triangular number?
736 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 736?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.