# Mathematics of Prime Divisibility Theorems: 10 Rules

As some have proposed, the division process might be sped up with divisibility criteria or tests. To find out which numbers may be evenly divided by others, we can use predetermined rules; for example, we can use the “government for 13” to find out which integers are divisible by 13. Realizing that there are only 2, 3, and 5 in that range, they realize their logic is simple.

However, Rules 7, 11, and 13 are more complex and need more study. Students can improve their problem-solving ability by learning the divisibility tests and division rules for the numbers 1 through 20. Get the results you need by using the divisible calculator.

Many people struggle with maths. Attempting to solve a mathematical issue can be challenging, and it might be tempting to resort to quick or simple methods. As a result, evaluation outcomes will strengthen. These rules are a great illustration of how such expedient measures might be implemented. Let’s take a look back at how division works in mathematics and go through some examples.

**Separation-Conquest (Division Rules in Maths)**

Mathematical tests and principles for divisibility can tell you if a number is divisible by another without actually having to split them. The quotient of an integer divided by another integer is always a whole number, and there is never any fractional part left behind.

Because no two numbers split into integers with a residual of zero, division by such a number is impossible. Applying certain principles to the digits of a number allows one to determine its divisor.

Including multiple real-world examples, this article provides a comprehensive breakdown of how to divide by integers from 1 to 13. Read on if you’re keen on mastering a speedy strategy for dividing large numbers.

**Division by Rule 1**

Any positive integer may be written as the sum of digits that split into one exactly. There are no restrictions on divisibility by 1 in the formula. A division by 1 always yields the same result, regardless of the size of the original integer. Both 3 and 3000 may be stated as a sum of ones, as is evident.

**Division by Rule 2**

All integers divisibility by two are even, including 2, 4, 6, 8, and 0.

An even number is 508, for instance. It’s thus divisible by 2, unlike the less exact 509.

There are a few techniques to determine if 508 is a divisor of 2:

There should be some thought given to the numbers. 508

The answer may be found by dividing the final digit (eight) by two.

This number is evenly divisible by two only if the last digit is an 8.

**Division by Rule 3**

An integer is said to be divisible by three only if the amount of its digits is also divisible by 3.

I’ve been using it on the number 308 as an illustration. Whether or whether 308 is divisible by three may be determined by adding up the digits (3+0+8=11). As a rule of thumb, it is a good number if the total can be divided by 3. The initial integer is divisible by three when the capacity is a multiple of three. The number 308 is similar to 11, which is not divisible by 3.

The sum of its digits, 5+1+6=12, is a multiple of 3, making 516 a perfect square.

**Division by Rule 4**

A number is a multiple of 4 and divisible by four if its final two digits are divisible by 4.

So, for instance, think of the year 2304 as an example. Remember that the final two digits sum up to 8. Number 2308 itself is divisible by four, much like the number 8.

**Dividing by the Rule 5**

Five can be subdivided into any integer that ends in zero or five.

Examples of such numbers include 10, 10,000, 1,000,000, 1,595,000, 394 000, 855 000, etc.

**Division by Rule 6 (Golden Law)**

Six-digit numbers can be evenly split into parts 2, 3, and themselves. The number is a multiple of 6 if and only if the last digit is an even integer and the sum of the numbers is a multiple of 3.

Due to the zero as the final digit, 630 is divisible by two but no other whole numbers.

Nine is a number that may be divided by both three and itself. The numbers are 6, 3, and 0.

Reason enough to divide 630 by 6.

**Division by Rule 7**

Stick to these steps, and you’ll quickly understand the 7-divide rule.

If you follow the rule, multiply the answer by 2, then subtract 3. Therefore the outcome is the number 6.

The result of subtracting 107 digits from a number is 1.

Another round of calculations yields the same result: 1 + 2 = 2.

Subtract two from 10, and you get 8.

Figure 1073 is not dividable by 7 in the same way that eight is not.

**Division by Rule 8**

An integer is dividable by 8 if and only if its final three digits may be divided by 8.

Consider the case of the number 24344. Just like 344 is divisible by 8, so is the original 24344. Look at the last two digits, 344, and ignore the rest.

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**Division by Rule 9**

The rule for determining if a figure is divisible by 9 is the same as deciding whether a number is divisible by 3. If the addition of its digits is divisible by 9, then that integer is said to be divisible by 9.

The sum of the digits in 78532, 25, is not divisible by nine; it is not a prime number.

**Division by Rule 10**

Any whole integer that ends in zero is divisible by 10.

The numbers 10, 20, 30, 1,000, 5,000, 60,000, etc.