31264
31264 is a even composite number that follows 31263 and precedes 31265. It is composed of 12 distinct factors: 1, 2, 4, 8, 16, 32, 977, 1954, 3908, 7816, 15632, 31264. Its prime factorization can be written as 2^5 × 977. 31264 is classified as a deficient number based on the sum of its proper divisors. In computer science, 31264 is represented as 111101000100000 in binary and 7A20 in hexadecimal.
Factor Analysis
12 FactorsProperties
The prime factorization (2^5 × 977) reveals 6 prime building blocks.
Divisible by 2
31264 ends in 4, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
31264 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 16 is not a multiple of 9.
Divisible by 10
31264 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Deficient classification and digit analytics place 31264 within several notable number theory sequences:
Timeline
Deep dive
How 31264 breaks down
31264 carries 12 distinct factors and a digit signature of 16 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 30350, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111101000100000 supports bitwise reasoning, hexadecimal 7A20 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 31264 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 31264 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (31259–31269) to tune search ranges, and educators feature 31264 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, Deficient numbers) help historians, numerologists, and trivia writers tie 31264 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 31264
Is 31264 a prime number?
31264 is composite with 12 total factors and the prime factorization 2^5 × 977.
What is the prime factorization of 31264?
It breaks down as 2^5 × 977, multiplying the primes 2 × 2 × 2 × 2 × 2 × 977.
How is 31264 represented in binary and hexadecimal?
31264 converts to 111101000100000 in binary and 7A20 in hexadecimal, which are helpful for computer science applications.
Is 31264 a perfect square, cube, or triangular number?
31264 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 31264?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.