144
144 is a even composite number that follows 143 and precedes 145. It is composed of 15 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Its prime factorization can be written as 2^4 × 3^2. 144 is classified as a abundant number based on the sum of its proper divisors. In computer science, 144 is represented as 10010000 in binary and 90 in hexadecimal. Historically, it is written as CXLIV in Roman numerals. It also belongs to the perfect square, Fibonacci number sequences.
Factor Analysis
15 FactorsProperties
The prime factorization (2^4 × 3^2) reveals 6 prime building blocks.
Divisible by 2
144 ends in 4, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 44 form a multiple of 4.
Divisible by 5
144 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 9 is a multiple of 9.
Divisible by 10
144 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 144 within several notable number theory sequences:
Timeline
Deep dive
How 144 breaks down
144 carries 15 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 259, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10010000 supports bitwise reasoning, hexadecimal 90 aligns with computing notation, and the Roman numeral CXLIV keeps the encyclopedic tradition alive. These attributes make 144 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 144 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (139–149) to tune search ranges, and educators feature 144 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, Perfect squares, Fibonacci numbers) help historians, numerologists, and trivia writers tie 144 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 144
Is 144 a prime number?
144 is composite with 15 total factors and the prime factorization 2^4 × 3^2.
What is the prime factorization of 144?
It breaks down as 2^4 × 3^2, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3.
How is 144 represented in binary and hexadecimal?
144 converts to 10010000 in binary and 90 in hexadecimal, which are helpful for computer science applications.
Is 144 a perfect square, cube, or triangular number?
144 is a perfect square, is not a perfect cube, and is not triangular. It also belongs to the Fibonacci sequence.
What are the digit sum and digital root of 144?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.