1500
1500 is a even composite number that follows 1499 and precedes 1501. It is composed of 24 distinct factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500. Its prime factorization can be written as 2^2 × 3 × 5^3. 1500 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1500 is represented as 10111011100 in binary and 5DC in hexadecimal. Historically, it is written as MD in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 3 × 5^3) reveals 6 prime building blocks.
Divisible by 2
1500 ends in 0, so it is even.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
1500 ends in 0, so it is divisible by 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 6 is not a multiple of 9.
Divisible by 10
1500 ends in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 1500 within several notable number theory sequences:
Timeline
Deep dive
How 1500 breaks down
1500 carries 24 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 2868, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10111011100 supports bitwise reasoning, hexadecimal 5DC aligns with computing notation, and the Roman numeral MD keeps the encyclopedic tradition alive. These attributes make 1500 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1500 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1495–1505) to tune search ranges, and educators feature 1500 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 1500 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 1500
Is 1500 a prime number?
1500 is composite with 24 total factors and the prime factorization 2^2 × 3 × 5^3.
What is the prime factorization of 1500?
It breaks down as 2^2 × 3 × 5^3, multiplying the primes 2 × 2 × 3 × 5 × 5 × 5.
How is 1500 represented in binary and hexadecimal?
1500 converts to 10111011100 in binary and 5DC in hexadecimal, which are helpful for computer science applications.
Is 1500 a perfect square, cube, or triangular number?
1500 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1500?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.