189
189 is a odd composite number that follows 188 and precedes 190. It is composed of 8 distinct factors: 1, 3, 7, 9, 21, 27, 63, 189. Its prime factorization can be written as 3^3 × 7. 189 is classified as a deficient number based on the sum of its proper divisors. In computer science, 189 is represented as 10111101 in binary and BD in hexadecimal. Historically, it is written as CLXXXIX in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (3^3 × 7) reveals 4 prime building blocks.
Divisible by 2
189 ends in 9, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 89 are not divisible by 4.
Divisible by 5
189 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 18 is a multiple of 9.
Divisible by 10
189 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Deficient classification and digit analytics place 189 within several notable number theory sequences:
Timeline
Deep dive
How 189 breaks down
189 carries 8 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 131, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10111101 supports bitwise reasoning, hexadecimal BD aligns with computing notation, and the Roman numeral CLXXXIX keeps the encyclopedic tradition alive. These attributes make 189 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 189 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (184–194) to tune search ranges, and educators feature 189 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, Deficient numbers) help historians, numerologists, and trivia writers tie 189 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 189
Is 189 a prime number?
189 is composite with 8 total factors and the prime factorization 3^3 × 7.
What is the prime factorization of 189?
It breaks down as 3^3 × 7, multiplying the primes 3 × 3 × 3 × 7.
How is 189 represented in binary and hexadecimal?
189 converts to 10111101 in binary and BD in hexadecimal, which are helpful for computer science applications.
Is 189 a perfect square, cube, or triangular number?
189 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 189?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.