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- Firstly it can divide two numbers.
- Secondly, it finds all the numbers by which a given number is divisible.
- Thirdly, it tells you if a given number is divisible by another number or not.

Any two numbers that can be divided into equal parts without leaving a leftover are said to be divisible. It means that if you divide one integer by another integer, the resulting number also be an integer to be considered divisible (whole positive number). If the result of the preceding division is not an integer, we can, if necessary, round it up to four digits.

By inspecting the digits of an integer, we can determine if it is divisible by a specified divisor using a divisibility rule, which is a kind of shortcut for determining divisibility. If a number is divisible by more than one rule, then its prime factorization can be found rapidly. Any positive integer that exactly halves the number is said to be a divisor of that number.

Famous mathematician and science writer Martin Gardner wrote about divisibility rules for 2–12 in a 1962 Scientific American article, explaining how they were commonly utilized during the Renaissance to simplify complex fractions. As a result, there is always the possibility of a non-zero remainder when dividing any two numbers. To get the true divisor of a number, we need only look at the digits within that number, and we can use certain principles to do so. These guidelines are known as divisibility rules.

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A divisibility rule is a method for quickly determining whether or not an integer is divisible by a particular divisor by inspecting the digits of the number itself, as opposed to doing the entire division operation.

The prime factorization of a number can be quickly determined by applying divisibility rules.

Any whole number that may be equally divided by another whole number is said to be a factor. Discovering the factors of a number requires us to know the divisors of that number.

For this, we use the rules of divisibility. We say that a number is divisible by it if it can be evenly divided into that number.

Let's understand this by an example. Suppose you and your brother or cousin want to divide up a sandwich, a pack of gum, or a plate of French fries such that no one is shorted: you are dealing with a divisible number of goods.

An integer is divisible by any multiple of that integer. For example, 28 is a multiple of 4 since it can be divided evenly by 4. Another way to look at it is that 28 is a multiple of 4 because it appears therein (in the 4's times table).

When dividing one integer by another, the quotient must be a whole number with no residual. The divisibility rules are shortcuts for finding a number's actual divisor by looking at its component digits because not all numbers are evenly divisible by other numbers.

If you can divide two numbers without a remainder, then the first number is divisible by the second. For example, 12 is divisible by 2. But 12 is not divisible by 5.