48
48 is a even composite number that follows 47 and precedes 49. It is composed of 10 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Its prime factorization can be written as 2^4 × 3. 48 is classified as a abundant number based on the sum of its proper divisors. In computer science, 48 is represented as 110000 in binary and 30 in hexadecimal. Historically, it is written as XLVIII in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 3) reveals 5 prime building blocks.
Divisible by 2
48 ends in 8, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 48 form a multiple of 4.
Divisible by 5
48 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 12 is not a multiple of 9.
Divisible by 10
48 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 48 within several notable number theory sequences:
Timeline
Deep dive
How 48 breaks down
48 carries 10 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 76, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110000 supports bitwise reasoning, hexadecimal 30 aligns with computing notation, and the Roman numeral XLVIII keeps the encyclopedic tradition alive. These attributes make 48 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 48 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (43–53) to tune search ranges, and educators feature 48 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, Abundant numbers) help historians, numerologists, and trivia writers tie 48 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 48
Is 48 a prime number?
48 is composite with 10 total factors and the prime factorization 2^4 × 3.
What is the prime factorization of 48?
It breaks down as 2^4 × 3, multiplying the primes 2 × 2 × 2 × 2 × 3.
How is 48 represented in binary and hexadecimal?
48 converts to 110000 in binary and 30 in hexadecimal, which are helpful for computer science applications.
Is 48 a perfect square, cube, or triangular number?
48 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 48?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.