78
78 is a even composite number that follows 77 and precedes 79. It is composed of 8 distinct factors: 1, 2, 3, 6, 13, 26, 39, 78. Its prime factorization can be written as 2 × 3 × 13. 78 is classified as a abundant number based on the sum of its proper divisors. In computer science, 78 is represented as 1001110 in binary and 4E in hexadecimal. Historically, it is written as LXXVIII in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 3 × 13) reveals 3 prime building blocks.
Divisible by 2
78 ends in 8, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 78 are not divisible by 4.
Divisible by 5
78 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 15 is not a multiple of 9.
Divisible by 10
78 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 78 within several notable number theory sequences:
Timeline
Deep dive
How 78 breaks down
78 carries 8 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 90, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1001110 supports bitwise reasoning, hexadecimal 4E aligns with computing notation, and the Roman numeral LXXVIII keeps the encyclopedic tradition alive. These attributes make 78 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 78 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (73–83) to tune search ranges, and educators feature 78 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 78 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 78
Is 78 a prime number?
78 is composite with 8 total factors and the prime factorization 2 × 3 × 13.
What is the prime factorization of 78?
It breaks down as 2 × 3 × 13, multiplying the primes 2 × 3 × 13.
How is 78 represented in binary and hexadecimal?
78 converts to 1001110 in binary and 4E in hexadecimal, which are helpful for computer science applications.
Is 78 a perfect square, cube, or triangular number?
78 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 78?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.