1488
1488 is a even composite number that follows 1487 and precedes 1489. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 31, 48, 62, 93, 124, 186, 248, 372, 496, 744, 1488. Its prime factorization can be written as 2^4 × 3 × 31. 1488 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1488 is represented as 10111010000 in binary and 5D0 in hexadecimal. Historically, it is written as MCDLXXXVIII in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 3 × 31) reveals 6 prime building blocks.
Divisible by 2
1488 ends in 8, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 88 form a multiple of 4.
Divisible by 5
1488 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 21 is not a multiple of 9.
Divisible by 10
1488 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 1488 within several notable number theory sequences:
Timeline
Deep dive
How 1488 breaks down
1488 carries 20 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 2480, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10111010000 supports bitwise reasoning, hexadecimal 5D0 aligns with computing notation, and the Roman numeral MCDLXXXVIII keeps the encyclopedic tradition alive. These attributes make 1488 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1488 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1483–1493) to tune search ranges, and educators feature 1488 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 1488 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 1488
Is 1488 a prime number?
1488 is composite with 20 total factors and the prime factorization 2^4 × 3 × 31.
What is the prime factorization of 1488?
It breaks down as 2^4 × 3 × 31, multiplying the primes 2 × 2 × 2 × 2 × 3 × 31.
How is 1488 represented in binary and hexadecimal?
1488 converts to 10111010000 in binary and 5D0 in hexadecimal, which are helpful for computer science applications.
Is 1488 a perfect square, cube, or triangular number?
1488 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1488?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.