2415
2415 is a odd composite number that follows 2414 and precedes 2416. It is composed of 16 distinct factors: 1, 3, 5, 7, 15, 21, 23, 35, 69, 105, 115, 161, 345, 483, 805, 2415. Its prime factorization can be written as 3 × 5 × 7 × 23. 2415 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2415 is represented as 100101101111 in binary and 96F in hexadecimal. Historically, it is written as MMCDXV in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
16 FactorsProperties
The prime factorization (3 × 5 × 7 × 23) reveals 4 prime building blocks.
Divisible by 2
2415 ends in 5, so it is odd.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 15 are not divisible by 4.
Divisible by 5
2415 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 12 is not a multiple of 9.
Divisible by 10
2415 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 2415 within several notable number theory sequences:
Timeline
Deep dive
How 2415 breaks down
2415 carries 16 distinct factors and a digit signature of 12 (3 as the digital root). The deficient classification indicates that its proper divisors sum to 2193, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100101101111 supports bitwise reasoning, hexadecimal 96F aligns with computing notation, and the Roman numeral MMCDXV keeps the encyclopedic tradition alive. These attributes make 2415 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2415 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2410–2420) to tune search ranges, and educators feature 2415 in worksheets about factor trees. Its binary footprint of length 12 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 2415 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 2415
Is 2415 a prime number?
2415 is composite with 16 total factors and the prime factorization 3 × 5 × 7 × 23.
What is the prime factorization of 2415?
It breaks down as 3 × 5 × 7 × 23, multiplying the primes 3 × 5 × 7 × 23.
How is 2415 represented in binary and hexadecimal?
2415 converts to 100101101111 in binary and 96F in hexadecimal, which are helpful for computer science applications.
Is 2415 a perfect square, cube, or triangular number?
2415 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 2415?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.