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Prime Number

3

3 is a odd prime number that follows 2 and precedes 4. As a prime number, 3 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 3. 3 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3 is represented as 11 in binary and 3 in hexadecimal. Historically, it is written as III in Roman numerals. It also belongs to the triangular number, Fibonacci number sequences.

Roman Numeral
III
LatinClassic
Binary
11
Base 2
Hexadecimal
3
Base 16

Factor Analysis

2 Factors

Properties

ParityOdd
Perfect SquareNo
Perfect CubeNo
Digit Count1
Digit Sum3
Digital Root3
Sum of Factors4
Aliquot Sum1
ClassificationDeficient
Prime Factors1
SequencesPrime numbers, Deficient numbers
Prime Factorization

3 is prime, so its only factors are 1 and 3.

Canonical form
3
3
Divisibility Insights
  • Divisible by 2

    3 ends in 3, so it is odd.

  • Divisible by 3

    The digit sum 3 is a multiple of 3.

  • Divisible by 4

    The last two digits 03 are not divisible by 4.

  • Divisible by 5

    3 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 3 is not a multiple of 9.

  • Divisible by 10

    3 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 3 within several notable number theory sequences:

Prime numbersDeficient numbersTriangular numbersFibonacci numbers

Timeline

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Deep dive

How 3 breaks down

3 carries 2 distinct factors and a digit signature of 3 (3 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 11 supports bitwise reasoning, hexadecimal 3 aligns with computing notation, and the Roman numeral III keeps the encyclopedic tradition alive. These attributes make 3 useful for math olympiad problems, puzzle design, and code challenges alike.

Context

Where 3 shows up

Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (18) to tune search ranges, and educators feature 3 in worksheets about prime identification. Its binary footprint of length 2 bits also makes it a solid example for teaching storage limits and overflow.

Beyond STEM, the classification and sequence tags (Prime numbers, Deficient numbers, Triangular numbers, Fibonacci numbers) help historians, numerologists, and trivia writers tie 3 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 3

Is 3 a prime number?

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

What is the prime factorization of 3?

3 is already prime, so the factorization is simply 3.

How is 3 represented in binary and hexadecimal?

3 converts to 11 in binary and 3 in hexadecimal, which are helpful for computer science applications.

Is 3 a perfect square, cube, or triangular number?

3 is not a perfect square, is not a perfect cube, and is triangular. It also belongs to the Fibonacci sequence.

What are the digit sum and digital root of 3?

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