156
156 is a even composite number that follows 155 and precedes 157. It is composed of 12 distinct factors: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156. Its prime factorization can be written as 2^2 × 3 × 13. 156 is classified as a abundant number based on the sum of its proper divisors. In computer science, 156 is represented as 10011100 in binary and 9C in hexadecimal. Historically, it is written as CLVI in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 3 × 13) reveals 4 prime building blocks.
Divisible by 2
156 ends in 6, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 56 form a multiple of 4.
Divisible by 5
156 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
156 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 156 within several notable number theory sequences:
Timeline
Deep dive
How 156 breaks down
156 carries 12 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 236, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10011100 supports bitwise reasoning, hexadecimal 9C aligns with computing notation, and the Roman numeral CLVI keeps the encyclopedic tradition alive. These attributes make 156 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 156 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (151–161) to tune search ranges, and educators feature 156 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 156 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 156
Is 156 a prime number?
156 is composite with 12 total factors and the prime factorization 2^2 × 3 × 13.
What is the prime factorization of 156?
It breaks down as 2^2 × 3 × 13, multiplying the primes 2 × 2 × 3 × 13.
How is 156 represented in binary and hexadecimal?
156 converts to 10011100 in binary and 9C in hexadecimal, which are helpful for computer science applications.
Is 156 a perfect square, cube, or triangular number?
156 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 156?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.