378
378 is a even composite number that follows 377 and precedes 379. It is composed of 16 distinct factors: 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378. Its prime factorization can be written as 2 × 3^3 × 7. 378 is classified as a abundant number based on the sum of its proper divisors. In computer science, 378 is represented as 101111010 in binary and 17A in hexadecimal. Historically, it is written as CCCLXXVIII in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
16 FactorsProperties
The prime factorization (2 × 3^3 × 7) reveals 5 prime building blocks.
Divisible by 2
378 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 78 are not divisible by 4.
Divisible by 5
378 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 18 is a multiple of 9.
Divisible by 10
378 does not end in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 378 within several notable number theory sequences:
Timeline
Deep dive
How 378 breaks down
378 carries 16 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 582, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101111010 supports bitwise reasoning, hexadecimal 17A aligns with computing notation, and the Roman numeral CCCLXXVIII keeps the encyclopedic tradition alive. These attributes make 378 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 378 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (373–383) to tune search ranges, and educators feature 378 in worksheets about factor trees. Its binary footprint of length 9 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 378 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 378
Is 378 a prime number?
378 is composite with 16 total factors and the prime factorization 2 × 3^3 × 7.
What is the prime factorization of 378?
It breaks down as 2 × 3^3 × 7, multiplying the primes 2 × 3 × 3 × 3 × 7.
How is 378 represented in binary and hexadecimal?
378 converts to 101111010 in binary and 17A in hexadecimal, which are helpful for computer science applications.
Is 378 a perfect square, cube, or triangular number?
378 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 378?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.