52
52 is a even composite number that follows 51 and precedes 53. It is composed of 6 distinct factors: 1, 2, 4, 13, 26, 52. Its prime factorization can be written as 2^2 × 13. 52 is classified as a deficient number based on the sum of its proper divisors. In computer science, 52 is represented as 110100 in binary and 34 in hexadecimal. Historically, it is written as LII in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (2^2 × 13) reveals 3 prime building blocks.
Divisible by 2
52 ends in 2, so it is even.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 52 form a multiple of 4.
Divisible by 5
52 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 7 is not a multiple of 9.
Divisible by 10
52 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Deficient classification and digit analytics place 52 within several notable number theory sequences:
Timeline
Deep dive
How 52 breaks down
52 carries 6 distinct factors and a digit signature of 7 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 46, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110100 supports bitwise reasoning, hexadecimal 34 aligns with computing notation, and the Roman numeral LII keeps the encyclopedic tradition alive. These attributes make 52 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 52 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (47–57) to tune search ranges, and educators feature 52 in worksheets about factor trees. Its binary footprint of length 6 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 52 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 52
Is 52 a prime number?
52 is composite with 6 total factors and the prime factorization 2^2 × 13.
What is the prime factorization of 52?
It breaks down as 2^2 × 13, multiplying the primes 2 × 2 × 13.
How is 52 represented in binary and hexadecimal?
52 converts to 110100 in binary and 34 in hexadecimal, which are helpful for computer science applications.
Is 52 a perfect square, cube, or triangular number?
52 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 52?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.