978
978 is a even composite number that follows 977 and precedes 979. It is composed of 8 distinct factors: 1, 2, 3, 6, 163, 326, 489, 978. Its prime factorization can be written as 2 × 3 × 163. 978 is classified as a abundant number based on the sum of its proper divisors. In computer science, 978 is represented as 1111010010 in binary and 3D2 in hexadecimal. Historically, it is written as CMLXXVIII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 3 × 163) reveals 3 prime building blocks.
Divisible by 2
978 ends in 8, so it is even.
Divisible by 3
The digit sum 24 is a multiple of 3.
Divisible by 4
The last two digits 78 are not divisible by 4.
Divisible by 5
978 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 24 is not a multiple of 9.
Divisible by 10
978 does not end in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Abundant classification and digit analytics place 978 within several notable number theory sequences:
Timeline
Deep dive
How 978 breaks down
978 carries 8 distinct factors and a digit signature of 24 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 990, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111010010 supports bitwise reasoning, hexadecimal 3D2 aligns with computing notation, and the Roman numeral CMLXXVIII keeps the encyclopedic tradition alive. These attributes make 978 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 978 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (973–983) to tune search ranges, and educators feature 978 in worksheets about factor trees. Its binary footprint of length 10 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 978 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 978
Is 978 a prime number?
978 is composite with 8 total factors and the prime factorization 2 × 3 × 163.
What is the prime factorization of 978?
It breaks down as 2 × 3 × 163, multiplying the primes 2 × 3 × 163.
How is 978 represented in binary and hexadecimal?
978 converts to 1111010010 in binary and 3D2 in hexadecimal, which are helpful for computer science applications.
Is 978 a perfect square, cube, or triangular number?
978 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 978?
The digits sum to 24, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.