177
177 is a odd composite number that follows 176 and precedes 178. It is composed of 4 distinct factors: 1, 3, 59, 177. Its prime factorization can be written as 3 × 59. 177 is classified as a deficient number based on the sum of its proper divisors. In computer science, 177 is represented as 10110001 in binary and B1 in hexadecimal. Historically, it is written as CLXXVII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (3 × 59) reveals 2 prime building blocks.
Divisible by 2
177 ends in 7, so it is odd.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 77 are not divisible by 4.
Divisible by 5
177 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 15 is not a multiple of 9.
Divisible by 10
177 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 177 within several notable number theory sequences:
Timeline
Deep dive
How 177 breaks down
177 carries 4 distinct factors and a digit signature of 15 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 63, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10110001 supports bitwise reasoning, hexadecimal B1 aligns with computing notation, and the Roman numeral CLXXVII keeps the encyclopedic tradition alive. These attributes make 177 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 177 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (172–182) to tune search ranges, and educators feature 177 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 177 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 177
Is 177 a prime number?
177 is composite with 4 total factors and the prime factorization 3 × 59.
What is the prime factorization of 177?
It breaks down as 3 × 59, multiplying the primes 3 × 59.
How is 177 represented in binary and hexadecimal?
177 converts to 10110001 in binary and B1 in hexadecimal, which are helpful for computer science applications.
Is 177 a perfect square, cube, or triangular number?
177 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 177?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.