174
174 is a even composite number that follows 173 and precedes 175. It is composed of 8 distinct factors: 1, 2, 3, 6, 29, 58, 87, 174. Its prime factorization can be written as 2 × 3 × 29. 174 is classified as a abundant number based on the sum of its proper divisors. In computer science, 174 is represented as 10101110 in binary and AE in hexadecimal. Historically, it is written as CLXXIV in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 3 × 29) reveals 3 prime building blocks.
Divisible by 2
174 ends in 4, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 74 are not divisible by 4.
Divisible by 5
174 does not end in 0 or 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 12 is not a multiple of 9.
Divisible by 10
174 does not end in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Abundant classification and digit analytics place 174 within several notable number theory sequences:
Timeline
Deep dive
How 174 breaks down
174 carries 8 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 186, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10101110 supports bitwise reasoning, hexadecimal AE aligns with computing notation, and the Roman numeral CLXXIV keeps the encyclopedic tradition alive. These attributes make 174 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 174 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (169–179) to tune search ranges, and educators feature 174 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 174 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 174
Is 174 a prime number?
174 is composite with 8 total factors and the prime factorization 2 × 3 × 29.
What is the prime factorization of 174?
It breaks down as 2 × 3 × 29, multiplying the primes 2 × 3 × 29.
How is 174 represented in binary and hexadecimal?
174 converts to 10101110 in binary and AE in hexadecimal, which are helpful for computer science applications.
Is 174 a perfect square, cube, or triangular number?
174 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 174?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.