37264
37264 is a even composite number that follows 37263 and precedes 37265. It is composed of 20 distinct factors: 1, 2, 4, 8, 16, 17, 34, 68, 136, 137, 272, 274, 548, 1096, 2192, 2329, 4658, 9316, 18632, 37264. Its prime factorization can be written as 2^4 × 17 × 137. 37264 is classified as a abundant number based on the sum of its proper divisors. In computer science, 37264 is represented as 1001000110010000 in binary and 9190 in hexadecimal.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 17 × 137) reveals 6 prime building blocks.
Divisible by 2
37264 ends in 4, so it is even.
Divisible by 3
The digit sum 22 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
37264 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 22 is not a multiple of 9.
Divisible by 10
37264 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 37264 within several notable number theory sequences:
Timeline
Deep dive
How 37264 breaks down
37264 carries 20 distinct factors and a digit signature of 22 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 39740, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1001000110010000 supports bitwise reasoning, hexadecimal 9190 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 37264 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 37264 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (37259–37269) to tune search ranges, and educators feature 37264 in worksheets about factor trees. Its binary footprint of length 16 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 37264 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 37264
Is 37264 a prime number?
37264 is composite with 20 total factors and the prime factorization 2^4 × 17 × 137.
What is the prime factorization of 37264?
It breaks down as 2^4 × 17 × 137, multiplying the primes 2 × 2 × 2 × 2 × 17 × 137.
How is 37264 represented in binary and hexadecimal?
37264 converts to 1001000110010000 in binary and 9190 in hexadecimal, which are helpful for computer science applications.
Is 37264 a perfect square, cube, or triangular number?
37264 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 37264?
The digits sum to 22, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.