676
676 is a even composite number that follows 675 and precedes 677. It is composed of 9 distinct factors: 1, 2, 4, 13, 26, 52, 169, 338, 676. Its prime factorization can be written as 2^2 × 13^2. 676 is classified as a deficient number based on the sum of its proper divisors. In computer science, 676 is represented as 1010100100 in binary and 2A4 in hexadecimal. Historically, it is written as DCLXXVI in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
9 FactorsProperties
The prime factorization (2^2 × 13^2) reveals 4 prime building blocks.
Divisible by 2
676 ends in 6, so it is even.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 76 form a multiple of 4.
Divisible by 5
676 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 19 is not a multiple of 9.
Divisible by 10
676 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Deficient classification and digit analytics place 676 within several notable number theory sequences:
Timeline
Deep dive
How 676 breaks down
676 carries 9 distinct factors and a digit signature of 19 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 605, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010100100 supports bitwise reasoning, hexadecimal 2A4 aligns with computing notation, and the Roman numeral DCLXXVI keeps the encyclopedic tradition alive. These attributes make 676 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 676 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (671–681) to tune search ranges, and educators feature 676 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, Deficient numbers, Perfect squares) help historians, numerologists, and trivia writers tie 676 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 676
Is 676 a prime number?
676 is composite with 9 total factors and the prime factorization 2^2 × 13^2.
What is the prime factorization of 676?
It breaks down as 2^2 × 13^2, multiplying the primes 2 × 2 × 13 × 13.
How is 676 represented in binary and hexadecimal?
676 converts to 1010100100 in binary and 2A4 in hexadecimal, which are helpful for computer science applications.
Is 676 a perfect square, cube, or triangular number?
676 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 676?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.