9072
9072 is a even composite number that follows 9071 and precedes 9073. It is composed of 50 distinct factors: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 81, 84, 108, 112, 126, 144, 162, 168, 189, 216, 252, 324, 336, 378, 432, 504, 567, 648, 756, 1008, 1134, 1296, 1512, 2268, 3024, 4536, 9072. Its prime factorization can be written as 2^4 × 3^4 × 7. 9072 is classified as a abundant number based on the sum of its proper divisors. In computer science, 9072 is represented as 10001101110000 in binary and 2370 in hexadecimal.
Factor Analysis
50 FactorsProperties
The prime factorization (2^4 × 3^4 × 7) reveals 9 prime building blocks.
Divisible by 2
9072 ends in 2, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
9072 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 18 is a multiple of 9.
Divisible by 10
9072 does not end in 0.
Divisible by 11
The alternating digit sum 14 is not a multiple of 11.
Abundant classification and digit analytics place 9072 within several notable number theory sequences:
Timeline
Deep dive
How 9072 breaks down
9072 carries 50 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 20936, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10001101110000 supports bitwise reasoning, hexadecimal 2370 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 9072 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 9072 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (9067–9077) to tune search ranges, and educators feature 9072 in worksheets about factor trees. Its binary footprint of length 14 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 9072 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 9072
Is 9072 a prime number?
9072 is composite with 50 total factors and the prime factorization 2^4 × 3^4 × 7.
What is the prime factorization of 9072?
It breaks down as 2^4 × 3^4 × 7, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 7.
How is 9072 represented in binary and hexadecimal?
9072 converts to 10001101110000 in binary and 2370 in hexadecimal, which are helpful for computer science applications.
Is 9072 a perfect square, cube, or triangular number?
9072 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 9072?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.