138
138 is a even composite number that follows 137 and precedes 139. It is composed of 8 distinct factors: 1, 2, 3, 6, 23, 46, 69, 138. Its prime factorization can be written as 2 × 3 × 23. 138 is classified as a abundant number based on the sum of its proper divisors. In computer science, 138 is represented as 10001010 in binary and 8A in hexadecimal. Historically, it is written as CXXXVIII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 3 × 23) reveals 3 prime building blocks.
Divisible by 2
138 ends in 8, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 38 are not divisible by 4.
Divisible by 5
138 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
138 does not end in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 138 within several notable number theory sequences:
Timeline
Deep dive
How 138 breaks down
138 carries 8 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 150, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10001010 supports bitwise reasoning, hexadecimal 8A aligns with computing notation, and the Roman numeral CXXXVIII keeps the encyclopedic tradition alive. These attributes make 138 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 138 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (133–143) to tune search ranges, and educators feature 138 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 138 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 138
Is 138 a prime number?
138 is composite with 8 total factors and the prime factorization 2 × 3 × 23.
What is the prime factorization of 138?
It breaks down as 2 × 3 × 23, multiplying the primes 2 × 3 × 23.
How is 138 represented in binary and hexadecimal?
138 converts to 10001010 in binary and 8A in hexadecimal, which are helpful for computer science applications.
Is 138 a perfect square, cube, or triangular number?
138 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 138?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.