164
164 is a even composite number that follows 163 and precedes 165. It is composed of 6 distinct factors: 1, 2, 4, 41, 82, 164. Its prime factorization can be written as 2^2 × 41. 164 is classified as a deficient number based on the sum of its proper divisors. In computer science, 164 is represented as 10100100 in binary and A4 in hexadecimal. Historically, it is written as CLXIV in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (2^2 × 41) reveals 3 prime building blocks.
Divisible by 2
164 ends in 4, so it is even.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
164 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 11 is not a multiple of 9.
Divisible by 10
164 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Deficient classification and digit analytics place 164 within several notable number theory sequences:
Timeline
Deep dive
How 164 breaks down
164 carries 6 distinct factors and a digit signature of 11 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 130, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10100100 supports bitwise reasoning, hexadecimal A4 aligns with computing notation, and the Roman numeral CLXIV keeps the encyclopedic tradition alive. These attributes make 164 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 164 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (159–169) to tune search ranges, and educators feature 164 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 164 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 164
Is 164 a prime number?
164 is composite with 6 total factors and the prime factorization 2^2 × 41.
What is the prime factorization of 164?
It breaks down as 2^2 × 41, multiplying the primes 2 × 2 × 41.
How is 164 represented in binary and hexadecimal?
164 converts to 10100100 in binary and A4 in hexadecimal, which are helpful for computer science applications.
Is 164 a perfect square, cube, or triangular number?
164 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 164?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.