675
675 is a odd composite number that follows 674 and precedes 676. It is composed of 12 distinct factors: 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675. Its prime factorization can be written as 3^3 × 5^2. 675 is classified as a deficient number based on the sum of its proper divisors. In computer science, 675 is represented as 1010100011 in binary and 2A3 in hexadecimal. Historically, it is written as DCLXXV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3^3 × 5^2) reveals 5 prime building blocks.
Divisible by 2
675 ends in 5, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 75 are not divisible by 4.
Divisible by 5
675 ends in 5, so it is divisible by 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
675 does not end in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Deficient classification and digit analytics place 675 within several notable number theory sequences:
Timeline
Deep dive
How 675 breaks down
675 carries 12 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 565, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010100011 supports bitwise reasoning, hexadecimal 2A3 aligns with computing notation, and the Roman numeral DCLXXV keeps the encyclopedic tradition alive. These attributes make 675 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 675 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (670–680) to tune search ranges, and educators feature 675 in worksheets about factor trees. Its binary footprint of length 10 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 675 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 675
Is 675 a prime number?
675 is composite with 12 total factors and the prime factorization 3^3 × 5^2.
What is the prime factorization of 675?
It breaks down as 3^3 × 5^2, multiplying the primes 3 × 3 × 3 × 5 × 5.
How is 675 represented in binary and hexadecimal?
675 converts to 1010100011 in binary and 2A3 in hexadecimal, which are helpful for computer science applications.
Is 675 a perfect square, cube, or triangular number?
675 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 675?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.