748
748 is a even composite number that follows 747 and precedes 749. It is composed of 12 distinct factors: 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748. Its prime factorization can be written as 2^2 × 11 × 17. 748 is classified as a abundant number based on the sum of its proper divisors. In computer science, 748 is represented as 1011101100 in binary and 2EC in hexadecimal. Historically, it is written as DCCXLVIII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 11 × 17) reveals 4 prime building blocks.
Divisible by 2
748 ends in 8, so it is even.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 48 form a multiple of 4.
Divisible by 5
748 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 19 is not a multiple of 9.
Divisible by 10
748 does not end in 0.
Divisible by 11
The alternating digit sum 11 is a multiple of 11.
Abundant classification and digit analytics place 748 within several notable number theory sequences:
Timeline
Deep dive
How 748 breaks down
748 carries 12 distinct factors and a digit signature of 19 (1 as the digital root). The abundant classification indicates that its proper divisors sum to 764, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011101100 supports bitwise reasoning, hexadecimal 2EC aligns with computing notation, and the Roman numeral DCCXLVIII keeps the encyclopedic tradition alive. These attributes make 748 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 748 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (743–753) to tune search ranges, and educators feature 748 in worksheets about factor trees. Its binary footprint of length 10 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 748 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 748
Is 748 a prime number?
748 is composite with 12 total factors and the prime factorization 2^2 × 11 × 17.
What is the prime factorization of 748?
It breaks down as 2^2 × 11 × 17, multiplying the primes 2 × 2 × 11 × 17.
How is 748 represented in binary and hexadecimal?
748 converts to 1011101100 in binary and 2EC in hexadecimal, which are helpful for computer science applications.
Is 748 a perfect square, cube, or triangular number?
748 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 748?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.