2478
2478 is a even composite number that follows 2477 and precedes 2479. It is composed of 16 distinct factors: 1, 2, 3, 6, 7, 14, 21, 42, 59, 118, 177, 354, 413, 826, 1239, 2478. Its prime factorization can be written as 2 × 3 × 7 × 59. 2478 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2478 is represented as 100110101110 in binary and 9AE in hexadecimal. Historically, it is written as MMCDLXXVIII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2 × 3 × 7 × 59) reveals 4 prime building blocks.
Divisible by 2
2478 ends in 8, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 78 are not divisible by 4.
Divisible by 5
2478 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 21 is not a multiple of 9.
Divisible by 10
2478 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 2478 within several notable number theory sequences:
Timeline
Deep dive
How 2478 breaks down
2478 carries 16 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 3282, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100110101110 supports bitwise reasoning, hexadecimal 9AE aligns with computing notation, and the Roman numeral MMCDLXXVIII keeps the encyclopedic tradition alive. These attributes make 2478 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2478 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2473–2483) to tune search ranges, and educators feature 2478 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, Abundant numbers) help historians, numerologists, and trivia writers tie 2478 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 2478
Is 2478 a prime number?
2478 is composite with 16 total factors and the prime factorization 2 × 3 × 7 × 59.
What is the prime factorization of 2478?
It breaks down as 2 × 3 × 7 × 59, multiplying the primes 2 × 3 × 7 × 59.
How is 2478 represented in binary and hexadecimal?
2478 converts to 100110101110 in binary and 9AE in hexadecimal, which are helpful for computer science applications.
Is 2478 a perfect square, cube, or triangular number?
2478 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2478?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.