17264
17264 is a even composite number that follows 17263 and precedes 17265. It is composed of 20 distinct factors: 1, 2, 4, 8, 13, 16, 26, 52, 83, 104, 166, 208, 332, 664, 1079, 1328, 2158, 4316, 8632, 17264. Its prime factorization can be written as 2^4 × 13 × 83. 17264 is classified as a abundant number based on the sum of its proper divisors. In computer science, 17264 is represented as 100001101110000 in binary and 4370 in hexadecimal.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 13 × 83) reveals 6 prime building blocks.
Divisible by 2
17264 ends in 4, so it is even.
Divisible by 3
The digit sum 20 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
17264 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 20 is not a multiple of 9.
Divisible by 10
17264 does not end in 0.
Divisible by 11
The alternating digit sum -6 is not a multiple of 11.
Abundant classification and digit analytics place 17264 within several notable number theory sequences:
Timeline
Deep dive
How 17264 breaks down
17264 carries 20 distinct factors and a digit signature of 20 (2 as the digital root). The abundant classification indicates that its proper divisors sum to 19192, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100001101110000 supports bitwise reasoning, hexadecimal 4370 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 17264 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 17264 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (17259–17269) to tune search ranges, and educators feature 17264 in worksheets about factor trees. Its binary footprint of length 15 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 17264 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 17264
Is 17264 a prime number?
17264 is composite with 20 total factors and the prime factorization 2^4 × 13 × 83.
What is the prime factorization of 17264?
It breaks down as 2^4 × 13 × 83, multiplying the primes 2 × 2 × 2 × 2 × 13 × 83.
How is 17264 represented in binary and hexadecimal?
17264 converts to 100001101110000 in binary and 4370 in hexadecimal, which are helpful for computer science applications.
Is 17264 a perfect square, cube, or triangular number?
17264 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 17264?
The digits sum to 20, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.