272
272 is a even composite number that follows 271 and precedes 273. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 17, 34, 68, 136, 272. Its prime factorization can be written as 2^4 × 17. 272 is classified as a abundant number based on the sum of its proper divisors. In computer science, 272 is represented as 100010000 in binary and 110 in hexadecimal. Historically, it is written as CCLXXII in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 17) reveals 5 prime building blocks.
Divisible by 2
272 ends in 2, so it is even.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
272 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
272 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 272 within several notable number theory sequences:
Timeline
Deep dive
How 272 breaks down
272 carries 10 distinct factors and a digit signature of 11 (2 as the digital root). The abundant classification indicates that its proper divisors sum to 286, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100010000 supports bitwise reasoning, hexadecimal 110 aligns with computing notation, and the Roman numeral CCLXXII keeps the encyclopedic tradition alive. These attributes make 272 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 272 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (267–277) to tune search ranges, and educators feature 272 in worksheets about factor trees. Its binary footprint of length 9 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 272 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 272
Is 272 a prime number?
272 is composite with 10 total factors and the prime factorization 2^4 × 17.
What is the prime factorization of 272?
It breaks down as 2^4 × 17, multiplying the primes 2 × 2 × 2 × 2 × 17.
How is 272 represented in binary and hexadecimal?
272 converts to 100010000 in binary and 110 in hexadecimal, which are helpful for computer science applications.
Is 272 a perfect square, cube, or triangular number?
272 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 272?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.