2072
2072 is a even composite number that follows 2071 and precedes 2073. It is composed of 16 distinct factors: 1, 2, 4, 7, 8, 14, 28, 37, 56, 74, 148, 259, 296, 518, 1036, 2072. Its prime factorization can be written as 2^3 × 7 × 37. 2072 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2072 is represented as 100000011000 in binary and 818 in hexadecimal. Historically, it is written as MMLXXII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 7 × 37) reveals 5 prime building blocks.
Divisible by 2
2072 ends in 2, so it is even.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
2072 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 11 is not a multiple of 9.
Divisible by 10
2072 does not end in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Abundant classification and digit analytics place 2072 within several notable number theory sequences:
Timeline
Deep dive
How 2072 breaks down
2072 carries 16 distinct factors and a digit signature of 11 (2 as the digital root). The abundant classification indicates that its proper divisors sum to 2488, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100000011000 supports bitwise reasoning, hexadecimal 818 aligns with computing notation, and the Roman numeral MMLXXII keeps the encyclopedic tradition alive. These attributes make 2072 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2072 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2067–2077) to tune search ranges, and educators feature 2072 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 2072 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 2072
Is 2072 a prime number?
2072 is composite with 16 total factors and the prime factorization 2^3 × 7 × 37.
What is the prime factorization of 2072?
It breaks down as 2^3 × 7 × 37, multiplying the primes 2 × 2 × 2 × 7 × 37.
How is 2072 represented in binary and hexadecimal?
2072 converts to 100000011000 in binary and 818 in hexadecimal, which are helpful for computer science applications.
Is 2072 a perfect square, cube, or triangular number?
2072 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2072?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.