5072
5072 is a even composite number that follows 5071 and precedes 5073. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 317, 634, 1268, 2536, 5072. Its prime factorization can be written as 2^4 × 317. 5072 is classified as a deficient number based on the sum of its proper divisors. In computer science, 5072 is represented as 1001111010000 in binary and 13D0 in hexadecimal.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 317) reveals 5 prime building blocks.
Divisible by 2
5072 ends in 2, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
5072 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
5072 does not end in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Deficient classification and digit analytics place 5072 within several notable number theory sequences:
Timeline
Deep dive
How 5072 breaks down
5072 carries 10 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 4786, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1001111010000 supports bitwise reasoning, hexadecimal 13D0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 5072 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 5072 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (5067–5077) to tune search ranges, and educators feature 5072 in worksheets about factor trees. Its binary footprint of length 13 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 5072 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 5072
Is 5072 a prime number?
5072 is composite with 10 total factors and the prime factorization 2^4 × 317.
What is the prime factorization of 5072?
It breaks down as 2^4 × 317, multiplying the primes 2 × 2 × 2 × 2 × 317.
How is 5072 represented in binary and hexadecimal?
5072 converts to 1001111010000 in binary and 13D0 in hexadecimal, which are helpful for computer science applications.
Is 5072 a perfect square, cube, or triangular number?
5072 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 5072?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.