407
407 is a odd composite number that follows 406 and precedes 408. It is composed of 4 distinct factors: 1, 11, 37, 407. Its prime factorization can be written as 11 × 37. 407 is classified as a deficient number based on the sum of its proper divisors. In computer science, 407 is represented as 110010111 in binary and 197 in hexadecimal. Historically, it is written as CDVII in Roman numerals.
Factor Analysis
4 FactorsProperties
The prime factorization (11 × 37) reveals 2 prime building blocks.
Divisible by 2
407 ends in 7, so it is odd.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 07 are not divisible by 4.
Divisible by 5
407 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 11 is not a multiple of 9.
Divisible by 10
407 does not end in 0.
Divisible by 11
The alternating digit sum 11 is a multiple of 11.
Deficient classification and digit analytics place 407 within several notable number theory sequences:
Timeline
Deep dive
How 407 breaks down
407 carries 4 distinct factors and a digit signature of 11 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 49, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110010111 supports bitwise reasoning, hexadecimal 197 aligns with computing notation, and the Roman numeral CDVII keeps the encyclopedic tradition alive. These attributes make 407 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 407 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (402–412) to tune search ranges, and educators feature 407 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, Deficient numbers) help historians, numerologists, and trivia writers tie 407 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 407
Is 407 a prime number?
407 is composite with 4 total factors and the prime factorization 11 × 37.
What is the prime factorization of 407?
It breaks down as 11 × 37, multiplying the primes 11 × 37.
How is 407 represented in binary and hexadecimal?
407 converts to 110010111 in binary and 197 in hexadecimal, which are helpful for computer science applications.
Is 407 a perfect square, cube, or triangular number?
407 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 407?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.