4072
4072 is a even composite number that follows 4071 and precedes 4073. It is composed of 8 distinct factors: 1, 2, 4, 8, 509, 1018, 2036, 4072. Its prime factorization can be written as 2^3 × 509. 4072 is classified as a deficient number based on the sum of its proper divisors. In computer science, 4072 is represented as 111111101000 in binary and FE8 in hexadecimal.
Factor Analysis
8 FactorsProperties
The prime factorization (2^3 × 509) reveals 4 prime building blocks.
Divisible by 2
4072 ends in 2, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
4072 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 13 is not a multiple of 9.
Divisible by 10
4072 does not end in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Deficient classification and digit analytics place 4072 within several notable number theory sequences:
Timeline
Deep dive
How 4072 breaks down
4072 carries 8 distinct factors and a digit signature of 13 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 3578, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111111101000 supports bitwise reasoning, hexadecimal FE8 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4072 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4072 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4067–4077) to tune search ranges, and educators feature 4072 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 4072 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 4072
Is 4072 a prime number?
4072 is composite with 8 total factors and the prime factorization 2^3 × 509.
What is the prime factorization of 4072?
It breaks down as 2^3 × 509, multiplying the primes 2 × 2 × 2 × 509.
How is 4072 represented in binary and hexadecimal?
4072 converts to 111111101000 in binary and FE8 in hexadecimal, which are helpful for computer science applications.
Is 4072 a perfect square, cube, or triangular number?
4072 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4072?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.