735
735 is a odd composite number that follows 734 and precedes 736. It is composed of 12 distinct factors: 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735. Its prime factorization can be written as 3 × 5 × 7^2. 735 is classified as a deficient number based on the sum of its proper divisors. In computer science, 735 is represented as 1011011111 in binary and 2DF in hexadecimal. Historically, it is written as DCCXXXV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3 × 5 × 7^2) reveals 4 prime building blocks.
Divisible by 2
735 ends in 5, so it is odd.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 35 are not divisible by 4.
Divisible by 5
735 ends in 5, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 15 is not a multiple of 9.
Divisible by 10
735 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 735 within several notable number theory sequences:
Timeline
Deep dive
How 735 breaks down
735 carries 12 distinct factors and a digit signature of 15 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 633, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011011111 supports bitwise reasoning, hexadecimal 2DF aligns with computing notation, and the Roman numeral DCCXXXV keeps the encyclopedic tradition alive. These attributes make 735 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 735 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (730–740) to tune search ranges, and educators feature 735 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 735 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 735
Is 735 a prime number?
735 is composite with 12 total factors and the prime factorization 3 × 5 × 7^2.
What is the prime factorization of 735?
It breaks down as 3 × 5 × 7^2, multiplying the primes 3 × 5 × 7 × 7.
How is 735 represented in binary and hexadecimal?
735 converts to 1011011111 in binary and 2DF in hexadecimal, which are helpful for computer science applications.
Is 735 a perfect square, cube, or triangular number?
735 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 735?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.