105
105 is a odd composite number that follows 104 and precedes 106. It is composed of 8 distinct factors: 1, 3, 5, 7, 15, 21, 35, 105. Its prime factorization can be written as 3 × 5 × 7. 105 is classified as a deficient number based on the sum of its proper divisors. In computer science, 105 is represented as 1101001 in binary and 69 in hexadecimal. Historically, it is written as CV in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 5 × 7) reveals 3 prime building blocks.
Divisible by 2
105 ends in 5, so it is odd.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 05 are not divisible by 4.
Divisible by 5
105 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 6 is not a multiple of 9.
Divisible by 10
105 does not end in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Deficient classification and digit analytics place 105 within several notable number theory sequences:
Timeline
Deep dive
How 105 breaks down
105 carries 8 distinct factors and a digit signature of 6 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 87, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1101001 supports bitwise reasoning, hexadecimal 69 aligns with computing notation, and the Roman numeral CV keeps the encyclopedic tradition alive. These attributes make 105 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 105 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (100–110) to tune search ranges, and educators feature 105 in worksheets about factor trees. Its binary footprint of length 7 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 105 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 105
Is 105 a prime number?
105 is composite with 8 total factors and the prime factorization 3 × 5 × 7.
What is the prime factorization of 105?
It breaks down as 3 × 5 × 7, multiplying the primes 3 × 5 × 7.
How is 105 represented in binary and hexadecimal?
105 converts to 1101001 in binary and 69 in hexadecimal, which are helpful for computer science applications.
Is 105 a perfect square, cube, or triangular number?
105 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 105?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.