Real numbers analyzer
Enter the number and we'll show you lot of information about that number, such as: is it a prime number, which number sets it belongs to (natural, integer, etc.), is it odd or even, positive or negative etc.

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Input data - enter your number you're going to analyze here

Your number

Results - what we can say about your number

Recognized number types
Is it natural numberyes
Is it integer numberyes
Is it real numberyes
Detected number sign
Is it positive numberyes
Is it negative numberno
Parity
Is number evenyes
Is number oddno
Various number forms
Number as decimal24
Number as fraction24
Factorization (natural numbers only)
no
2 × 2 × 2 × 3
23 × 3
Number in words
Number in words (digit by digit)two four
Number in words (whole number at once)twenty-four

Some facts

  • Natural numbers is the most intuitive set of numbers. This is the first kind of numbers that we meet at school, because they have a direct impact on the reality that surrounds us. Natural numbers are used during counting or ordering items.
    ⓘ Example: "You want one or two scoops of ice cream?" - mom asked.
    "Three, three, or better four!" - Andrew replied.
  • If we extend the natural numbers by negative numbers, then we get the set of integer numbers.
    ⓘ Example: During the so-called winter of the century was exceptionally cold. In some regions of Poland the temperature dropped even to -30 °C.
  • If we combine two integers into a fraction , we get a set of rational numbers:
    rational number=integer numberinteger number\text{rational number} = \dfrac{\text{integer number}}{\text{integer number}}
    ⓘ Example: There are 25 people in Rose's class, of which 12 are boys, and 13 are girls. This means that 1225\dfrac{12}{25} of all pupils are boys and 1325\dfrac{13}{25} are girls.
  • All the above numbers have a common feature: they can be placed on the number axis. However, it turns out there are numbers, that can be placed on the axis, but can not be represented as the ratio of two integers. They are so-called irrational numbers. If we combine all rational and irrational numbers together, we get a set of real numbers.
    ⓘ Example: The number π is an irrational number, because it can not be represented as a ratio of two integers. Nevertheless, it can still be placed on the number axis after the number 3 and before the number 4. The approximate value of π is 3.14.
  • The above numerical sets have their typical symbols:
    • the natural numbers set: N={1,2,3,4,5,...}\N = \{1, 2, 3, 4, 5, ...\},
    • the integer numbers set: Z={...,2,1,0,1,2,...}\Z = \{..., -2, -1, 0, 1, 2, ...\},
    • the rational numbers set: Q={pq:p,qZ,q0}\mathbb Q = \left\{ \dfrac{p}{q} : p, q \in \mathbb Z, q \ne 0 \right\},
    • the real numbers set: R\R.
  • Sometimes we also include the number zero (0) in the set of natural numbers. However, this does not follow any strict rules, but it results from the practical considerations. Therefore, we can define natural numbers in two ways:
    • without zero: N={1,2,3,4,5,...}\N = \{1, 2, 3, 4, 5, ...\},
    • with zero N={0,1,2,3,4,5,...}\N = \{0, 1, 2, 3, 4, 5, ...\}.
  • Since both definitions are valid, sometimes - to avoid misunderstanding - we define natural numbers on the basis of integers:
    • natural numbers without zero are the same as positive integers:
      Z+={1,2,3,4,5,...}\Z_{+} = \{1, 2, 3, 4, 5, ...\}
    • natural numbers with zero are the same as positive integers with zero added:
      Z+{0}={0,1,2,3,4,5,...}\Z_{+} \cup \{0\} = \{0, 1, 2, 3, 4, 5, ...\}

What is the meaning of each calculator field ?

  • Recognized number types:
    • is it natural number - shows if the given number belongs to the set of natural numbers N={1,2,3,4,5,...}\N = \{1, 2, 3, 4, 5, ... \}, for this calculator we assume that the number zero (0) is not natural,
    • is it integer number - shows whether the given number belongs to a set of integers Z={...,2,1,0,1,2,...}\Z = \{..., -2, -1, 0, 1, 2, ...\},
    • is it real number - shows whether the given number belongs to the set of real numbers R\R,
  • detected number sign:
    • is it positive number - shows if the given number is greater than zero,
    • is it negative number - shows if the number is less than zero,
  • parity:
    • is even number - shows whether the given number is divisible by 2 (the remainder of dividing by two is zero),
    • is odd number - shows if the given number is indivisible by 2 (the remainder of dividing by two is non-zero),
  • various number forms:
    • number as decimal - Your number presented in decimal fraction form, e.g. 3.14,
    • number as fraction - Your number presented in simple fraction form (with fraction slash) e.g. 3141003 \dfrac{14}{100}, if you would like to know more about fractions, you can check out our other calculator: Fractions
  • factorization (natural numbers only):
    • is prime - shows if the given number is a prime number, primes are numbers that have exactly two divisors (colloquially: they are divisible only by one and by themselves), you can find out more about prime numbers by visiting our other calculator: Prime number,
    • factorization - the number presented as the product of prime numbers, the same number may occur more than once, e.g. 144=222233144 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3,
    • grouped factors - the number presented as the product of prime numbers, but with repeated factors replaced by by exponentiation, e.g. 144=2432144 = 2^4 \cdot 3^2
  • number in words:
    • digit by digit - number read in words as a list of separated digits, e.g. three point one four,
    • whole number at once - number read in words at once e.g. three and fourteen hundreds, if you want to learn more about the numbers grammar you can visit our other calculator: Number to words

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