1407
1407 is a odd composite number that follows 1406 and precedes 1408. It is composed of 8 distinct factors: 1, 3, 7, 21, 67, 201, 469, 1407. Its prime factorization can be written as 3 × 7 × 67. 1407 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1407 is represented as 10101111111 in binary and 57F in hexadecimal. Historically, it is written as MCDVII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 7 × 67) reveals 3 prime building blocks.
Divisible by 2
1407 ends in 7, so it is odd.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 07 are not divisible by 4.
Divisible by 5
1407 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 12 is not a multiple of 9.
Divisible by 10
1407 does not end in 0.
Divisible by 11
The alternating digit sum -10 is not a multiple of 11.
Deficient classification and digit analytics place 1407 within several notable number theory sequences:
Timeline
Deep dive
How 1407 breaks down
1407 carries 8 distinct factors and a digit signature of 12 (3 as the digital root). The deficient classification indicates that its proper divisors sum to 769, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10101111111 supports bitwise reasoning, hexadecimal 57F aligns with computing notation, and the Roman numeral MCDVII keeps the encyclopedic tradition alive. These attributes make 1407 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1407 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1402–1412) to tune search ranges, and educators feature 1407 in worksheets about factor trees. Its binary footprint of length 11 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 1407 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 1407
Is 1407 a prime number?
1407 is composite with 8 total factors and the prime factorization 3 × 7 × 67.
What is the prime factorization of 1407?
It breaks down as 3 × 7 × 67, multiplying the primes 3 × 7 × 67.
How is 1407 represented in binary and hexadecimal?
1407 converts to 10101111111 in binary and 57F in hexadecimal, which are helpful for computer science applications.
Is 1407 a perfect square, cube, or triangular number?
1407 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1407?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.