150
150 is a even composite number that follows 149 and precedes 151. It is composed of 12 distinct factors: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150. Its prime factorization can be written as 2 × 3 × 5^2. 150 is classified as a abundant number based on the sum of its proper divisors. In computer science, 150 is represented as 10010110 in binary and 96 in hexadecimal. Historically, it is written as CL in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 3 × 5^2) reveals 4 prime building blocks.
Divisible by 2
150 ends in 0, so it is even.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 50 are not divisible by 4.
Divisible by 5
150 ends in 0, so it is divisible by 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 6 is not a multiple of 9.
Divisible by 10
150 ends in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 150 within several notable number theory sequences:
Timeline
Deep dive
How 150 breaks down
150 carries 12 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 222, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10010110 supports bitwise reasoning, hexadecimal 96 aligns with computing notation, and the Roman numeral CL keeps the encyclopedic tradition alive. These attributes make 150 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 150 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (145–155) to tune search ranges, and educators feature 150 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 150 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 150
Is 150 a prime number?
150 is composite with 12 total factors and the prime factorization 2 × 3 × 5^2.
What is the prime factorization of 150?
It breaks down as 2 × 3 × 5^2, multiplying the primes 2 × 3 × 5 × 5.
How is 150 represented in binary and hexadecimal?
150 converts to 10010110 in binary and 96 in hexadecimal, which are helpful for computer science applications.
Is 150 a perfect square, cube, or triangular number?
150 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 150?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.