120
120 is a even composite number that follows 119 and precedes 121. It is composed of 16 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Its prime factorization can be written as 2^3 × 3 × 5. 120 is classified as a abundant number based on the sum of its proper divisors. In computer science, 120 is represented as 1111000 in binary and 78 in hexadecimal. Historically, it is written as CXX in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 5) reveals 5 prime building blocks.
Divisible by 2
120 ends in 0, so it is even.
Divisible by 3
The digit sum 3 is a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
120 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 3 is not a multiple of 9.
Divisible by 10
120 ends in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 120 within several notable number theory sequences:
Timeline
Deep dive
How 120 breaks down
120 carries 16 distinct factors and a digit signature of 3 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 240, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111000 supports bitwise reasoning, hexadecimal 78 aligns with computing notation, and the Roman numeral CXX keeps the encyclopedic tradition alive. These attributes make 120 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 120 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (115–125) to tune search ranges, and educators feature 120 in worksheets about factor trees. Its binary footprint of length 7 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Abundant numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 120 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 120
Is 120 a prime number?
120 is composite with 16 total factors and the prime factorization 2^3 × 3 × 5.
What is the prime factorization of 120?
It breaks down as 2^3 × 3 × 5, multiplying the primes 2 × 2 × 2 × 3 × 5.
How is 120 represented in binary and hexadecimal?
120 converts to 1111000 in binary and 78 in hexadecimal, which are helpful for computer science applications.
Is 120 a perfect square, cube, or triangular number?
120 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 120?
The digits sum to 3, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.