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Prime Number

4007

4007 is a odd prime number that follows 4006 and precedes 4008. As a prime number, 4007 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 4007. 4007 is classified as a deficient number based on the sum of its proper divisors. In computer science, 4007 is represented as 111110100111 in binary and FA7 in hexadecimal.

Roman Numeral
N/A (1-3999)
LatinClassic
Binary
111110100111
Base 2
Hexadecimal
FA7
Base 16

Factor Analysis

2 Factors

Properties

ParityOdd
Perfect SquareNo
Perfect CubeNo
Digit Count4
Digit Sum11
Digital Root2
Sum of Factors4008
Aliquot Sum1
ClassificationDeficient
Prime Factors1
SequencesPrime numbers, Deficient numbers
Prime Factorization

4007 is prime, so its only factors are 1 and 4007.

Canonical form
4007
4007
Divisibility Insights
  • Divisible by 2

    4007 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

    4007 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

    4007 does not end in 0.

  • Divisible by 11

    The alternating digit sum -3 is not a multiple of 11.

Sequence Membership

Deficient classification and digit analytics place 4007 within several notable number theory sequences:

Prime numbersDeficient numbers
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Deep dive

How 4007 breaks down

4007 carries 2 distinct factors and a digit signature of 11 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.

Numeral conversions provide additional context: the binary form 111110100111 supports bitwise reasoning, hexadecimal FA7 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4007 useful for math olympiad problems, puzzle design, and code challenges alike.

Context

Where 4007 shows up

Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (40024012) to tune search ranges, and educators feature 4007 in worksheets about prime identification. Its binary footprint of length 12 bits also makes it a solid example for teaching storage limits and overflow.

Beyond STEM, the classification and sequence tags (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 4007 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 4007

Is 4007 a prime number?

4007 is prime, meaning it is only divisible by 1 and itself.

What is the prime factorization of 4007?

4007 is already prime, so the factorization is simply 4007.

How is 4007 represented in binary and hexadecimal?

4007 converts to 111110100111 in binary and FA7 in hexadecimal, which are helpful for computer science applications.

Is 4007 a perfect square, cube, or triangular number?

4007 is not a perfect square, is not a perfect cube, and is not triangular.

What are the digit sum and digital root of 4007?

The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.