DIVISIBILITY RULES - FOR 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 AND PRIME DIVISORS 13 TO 47 AND ABOVE

Please study Multiplication Tables and
Division before Divisibility Rules
They are prerequisites here.

Here we study methods that can be used to determine
whether a number is evenly divisible by other numbers.

These are shortcuts for testing a number's factors
without resorting to division calculations.

The rules given below transform a given number's divisibility
by a divisor to a smaller number's divisibility by the same divisor.

If the result is not obvious after applying it once,
the rule should be applied again to the smaller number.

We present the rules with examples, in a simple way,
to follow, understand and apply.

We provide the rules for all the single digit divisors
and prime divisors upto 47 and above
and a general method which is simple to use.

Divisibility Rules for 2 and 4

Given below is the Link for
Divisibility Rules for 2 and 4
Divisibility by 2 and 4

Divisibility Rule for 3 :

A number is divisible by 3, if the number obtained by adding its digits is divisible by 3.
If you don't know the new number's divisibility, you can apply the rule again.

Find whether 23451 is divisible by 3 or not.

Solution :
The number formed by sum of the digits = 2 + 3 + 4 + 5 + 1 = 15.
We know 15 is divisible by 3.
∴ 23451 is divisible by 3. Ans.

Example 2 of Rule of Divisibility for 3

Find whether 142367 is divisible by 3 or not.

Solution :
The number formed by sum of the digits = 1 + 4 + 2 + 3 + 6 + 7 = 23.
We know 23 is not divisible by 3.
∴ 142367 is not divisible by 3. Ans.

Example 3 of Divisibility Rule for 3

Find whether 652743 is divisible by 3 or not.

Solution :
The number formed by sum of the digits = 6 + 5 + 2 + 7 + 4 + 3 = 27.
We know 27 is divisible by 3.
∴ 652743 is divisible by 3. Ans.

Example 4 of Divisibility Rule for 3

Find whether 5230716 is divisible by 3 or not.

Solution :
The number formed by sum of the digits = 5 + 2 + 3 + 0 + 7 + 1 + 6 = 24.
We know 24 is divisible by 3.
∴ 5230716 is divisible by 3. Ans.

Example 5 of Divisibility Rule for 3

Find whether 91451080 is divisible by 3 or not.

Solution :
The number formed by sum of the digits = 9 + 1 + 4 + 5 + 1 + 0 + 8 + 0 = 29.
We know 28 is not divisible by 3.
∴ 91451080 is not divisible by 3. Ans. Great Deals on School & Homeschool Curriculum Books

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Divisibility Rule for 6

A number is divisible by 6, if the number is divisible by both 2 and 3.

Examples:
check whether the Numbers in examples under divisibility by 3, are divisible by 6 or not.

Solution:
Here, we have to first check whether the number is even or odd.
If it is odd, then it is not divisible by 6.

If it is even, then check for the divisibility by 3. If it is divisible by 3,
then it is divisible by 6. Otherwise not.

In the above examples under divisibility by 3,
Numbers in Examples 1, 2, 3 are odd numbers
and hence are not divisible by 6.

Out of Numbers in remaining Examples 4 and 5,
Number in Example 5 is not divisible by 3.

∴ only Number in Example 4 is divisible by 6.









Given below are the Links for
Rules of Divisibility for 5, 7, 8, 9, 10, 11
and Rules of Divisibility for any Prime Divisor.

Divisibility by 5, 9 and 10

Divisibility by 7

Divisibility by 8

Divisibility by 11

Divisibility Test for 2 to 11

Divisibility by Prime Divisor

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