90
90 is a even composite number that follows 89 and precedes 91. It is composed of 12 distinct factors: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. Its prime factorization can be written as 2 × 3^2 × 5. 90 is classified as a abundant number based on the sum of its proper divisors. In computer science, 90 is represented as 1011010 in binary and 5A in hexadecimal. Historically, it is written as XC in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 3^2 × 5) reveals 4 prime building blocks.
Divisible by 2
90 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 90 are not divisible by 4.
Divisible by 5
90 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
90 ends in 0.
Divisible by 11
The alternating digit sum 9 is not a multiple of 11.
Abundant classification and digit analytics place 90 within several notable number theory sequences:
Timeline
Deep dive
How 90 breaks down
90 carries 12 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 144, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011010 supports bitwise reasoning, hexadecimal 5A aligns with computing notation, and the Roman numeral XC keeps the encyclopedic tradition alive. These attributes make 90 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 90 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (85–95) to tune search ranges, and educators feature 90 in worksheets about factor trees. Its binary footprint of length 7 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 90 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 90
Is 90 a prime number?
90 is composite with 12 total factors and the prime factorization 2 × 3^2 × 5.
What is the prime factorization of 90?
It breaks down as 2 × 3^2 × 5, multiplying the primes 2 × 3 × 3 × 5.
How is 90 represented in binary and hexadecimal?
90 converts to 1011010 in binary and 5A in hexadecimal, which are helpful for computer science applications.
Is 90 a perfect square, cube, or triangular number?
90 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 90?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.