450
450 is a even composite number that follows 449 and precedes 451. It is composed of 18 distinct factors: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450. Its prime factorization can be written as 2 × 3^2 × 5^2. 450 is classified as a abundant number based on the sum of its proper divisors. In computer science, 450 is represented as 111000010 in binary and 1C2 in hexadecimal. Historically, it is written as CDL in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2 × 3^2 × 5^2) reveals 5 prime building blocks.
Divisible by 2
450 ends in 0, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 50 are not divisible by 4.
Divisible by 5
450 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 9 is a multiple of 9.
Divisible by 10
450 ends in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 450 within several notable number theory sequences:
Timeline
Deep dive
How 450 breaks down
450 carries 18 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 759, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111000010 supports bitwise reasoning, hexadecimal 1C2 aligns with computing notation, and the Roman numeral CDL keeps the encyclopedic tradition alive. These attributes make 450 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 450 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (445–455) to tune search ranges, and educators feature 450 in worksheets about factor trees. Its binary footprint of length 9 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 450 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 450
Is 450 a prime number?
450 is composite with 18 total factors and the prime factorization 2 × 3^2 × 5^2.
What is the prime factorization of 450?
It breaks down as 2 × 3^2 × 5^2, multiplying the primes 2 × 3 × 3 × 5 × 5.
How is 450 represented in binary and hexadecimal?
450 converts to 111000010 in binary and 1C2 in hexadecimal, which are helpful for computer science applications.
Is 450 a perfect square, cube, or triangular number?
450 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 450?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.