2516
2516 is a even composite number that follows 2515 and precedes 2517. It is composed of 12 distinct factors: 1, 2, 4, 17, 34, 37, 68, 74, 148, 629, 1258, 2516. Its prime factorization can be written as 2^2 × 17 × 37. 2516 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2516 is represented as 100111010100 in binary and 9D4 in hexadecimal. Historically, it is written as MMDXVI in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 17 × 37) reveals 4 prime building blocks.
Divisible by 2
2516 ends in 6, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 16 form a multiple of 4.
Divisible by 5
2516 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 14 is not a multiple of 9.
Divisible by 10
2516 does not end in 0.
Divisible by 11
The alternating digit sum -8 is not a multiple of 11.
Deficient classification and digit analytics place 2516 within several notable number theory sequences:
Timeline
Deep dive
How 2516 breaks down
2516 carries 12 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 2272, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100111010100 supports bitwise reasoning, hexadecimal 9D4 aligns with computing notation, and the Roman numeral MMDXVI keeps the encyclopedic tradition alive. These attributes make 2516 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2516 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2511–2521) to tune search ranges, and educators feature 2516 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) help historians, numerologists, and trivia writers tie 2516 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 2516
Is 2516 a prime number?
2516 is composite with 12 total factors and the prime factorization 2^2 × 17 × 37.
What is the prime factorization of 2516?
It breaks down as 2^2 × 17 × 37, multiplying the primes 2 × 2 × 17 × 37.
How is 2516 represented in binary and hexadecimal?
2516 converts to 100111010100 in binary and 9D4 in hexadecimal, which are helpful for computer science applications.
Is 2516 a perfect square, cube, or triangular number?
2516 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2516?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.