3978
3978 is a even composite number that follows 3977 and precedes 3979. It is composed of 24 distinct factors: 1, 2, 3, 6, 9, 13, 17, 18, 26, 34, 39, 51, 78, 102, 117, 153, 221, 234, 306, 442, 663, 1326, 1989, 3978. Its prime factorization can be written as 2 × 3^2 × 13 × 17. 3978 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3978 is represented as 111110001010 in binary and F8A in hexadecimal. Historically, it is written as MMMCMLXXVIII in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2 × 3^2 × 13 × 17) reveals 5 prime building blocks.
Divisible by 2
3978 ends in 8, so it is even.
Divisible by 3
The digit sum 27 is a multiple of 3.
Divisible by 4
The last two digits 78 are not divisible by 4.
Divisible by 5
3978 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 27 is a multiple of 9.
Divisible by 10
3978 does not end in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Abundant classification and digit analytics place 3978 within several notable number theory sequences:
Timeline
Deep dive
How 3978 breaks down
3978 carries 24 distinct factors and a digit signature of 27 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 5850, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111110001010 supports bitwise reasoning, hexadecimal F8A aligns with computing notation, and the Roman numeral MMMCMLXXVIII keeps the encyclopedic tradition alive. These attributes make 3978 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3978 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3973–3983) to tune search ranges, and educators feature 3978 in worksheets about factor trees. Its binary footprint of length 12 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 3978 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 3978
Is 3978 a prime number?
3978 is composite with 24 total factors and the prime factorization 2 × 3^2 × 13 × 17.
What is the prime factorization of 3978?
It breaks down as 2 × 3^2 × 13 × 17, multiplying the primes 2 × 3 × 3 × 13 × 17.
How is 3978 represented in binary and hexadecimal?
3978 converts to 111110001010 in binary and F8A in hexadecimal, which are helpful for computer science applications.
Is 3978 a perfect square, cube, or triangular number?
3978 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3978?
The digits sum to 27, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.