1248
1248 is a even composite number that follows 1247 and precedes 1249. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 78, 96, 104, 156, 208, 312, 416, 624, 1248. Its prime factorization can be written as 2^5 × 3 × 13. 1248 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1248 is represented as 10011100000 in binary and 4E0 in hexadecimal. Historically, it is written as MCCXLVIII in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^5 × 3 × 13) reveals 7 prime building blocks.
Divisible by 2
1248 ends in 8, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 48 form a multiple of 4.
Divisible by 5
1248 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 15 is not a multiple of 9.
Divisible by 10
1248 does not end in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Abundant classification and digit analytics place 1248 within several notable number theory sequences:
Timeline
Deep dive
How 1248 breaks down
1248 carries 24 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 2280, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10011100000 supports bitwise reasoning, hexadecimal 4E0 aligns with computing notation, and the Roman numeral MCCXLVIII keeps the encyclopedic tradition alive. These attributes make 1248 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1248 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1243–1253) to tune search ranges, and educators feature 1248 in worksheets about factor trees. Its binary footprint of length 11 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 1248 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 1248
Is 1248 a prime number?
1248 is composite with 24 total factors and the prime factorization 2^5 × 3 × 13.
What is the prime factorization of 1248?
It breaks down as 2^5 × 3 × 13, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 13.
How is 1248 represented in binary and hexadecimal?
1248 converts to 10011100000 in binary and 4E0 in hexadecimal, which are helpful for computer science applications.
Is 1248 a perfect square, cube, or triangular number?
1248 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1248?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.