180
180 is a even composite number that follows 179 and precedes 181. It is composed of 18 distinct factors: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. Its prime factorization can be written as 2^2 × 3^2 × 5. 180 is classified as a abundant number based on the sum of its proper divisors. In computer science, 180 is represented as 10110100 in binary and B4 in hexadecimal. Historically, it is written as CLXXX in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^2 × 3^2 × 5) reveals 5 prime building blocks.
Divisible by 2
180 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 80 form a multiple of 4.
Divisible by 5
180 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
180 ends in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Abundant classification and digit analytics place 180 within several notable number theory sequences:
Timeline
Deep dive
How 180 breaks down
180 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 366, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10110100 supports bitwise reasoning, hexadecimal B4 aligns with computing notation, and the Roman numeral CLXXX keeps the encyclopedic tradition alive. These attributes make 180 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 180 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (175–185) to tune search ranges, and educators feature 180 in worksheets about factor trees. Its binary footprint of length 8 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 180 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 180
Is 180 a prime number?
180 is composite with 18 total factors and the prime factorization 2^2 × 3^2 × 5.
What is the prime factorization of 180?
It breaks down as 2^2 × 3^2 × 5, multiplying the primes 2 × 2 × 3 × 3 × 5.
How is 180 represented in binary and hexadecimal?
180 converts to 10110100 in binary and B4 in hexadecimal, which are helpful for computer science applications.
Is 180 a perfect square, cube, or triangular number?
180 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 180?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.