This topic deals with the properties of divisibility which will help us in doing our multiplication and division easy. These rules will help us to determine quickly the factors of certain number, the divisibility criteria of certain number and helps in overall strengthening the knowledge and concepts of mathematics.
Divisibility Property I:
The factor of a number is divisible by that given number (N) and is also divisible by any multiple of the given number (N).
Example Justifying the Property
1. 4 is a factor of 12
4 is divisible by 12. As 12/4 = 3
Now 4 is a factor of any multiple of 12
We know that 12 × 11 = 132
So, 132 is also divisible by 4. 132/4 = 44
2. 11 is a factor of 121
As 121 divided by 11 is 11
Now 11 is a factor of any multiple of 121
Now 121 × 9 = 1089
So, 1089 is also divisible by 11. 1089 /11 gives 99 as quotient
Divisibility Property II:
Let N be a number and is divisible by say M. Then N is divisible by all the factors of M.
Example Justifying the Property:
1. 144 is divisible by 12. As, 144/12 = 12
Now the factors of 12 are 1, 2, 3, 4, 6, 12
So 144 is divisible by all the factors
144 ÷ 2 = 72
144 ÷ 3 = 48
144 ÷ 4 = 36
144 ÷ 6 = 24
2. 126 is divisible by 14
The factors of 14 are 1, 2, 7, 14
126 is also divisible by 2 and 7
126 ÷ 2 = 63
126 ÷ 7 = 18
Divisibility Property III:
If a number (N) is divisible by two co-prime number then the given number (N) is also divisible by the product of the two co-prime numbers
Example Justifying the Property:
1. 36 is divisible by 2 and 3. And 2 and 3 are co-prime.
Product of 2 and 3 = 6
So according to the property 36 is also divisible by 6
2. 24 is divisible by both 3 and 4 and they are co prime
Product of 3 and 4 = 12
24 is also divisible by 12
Divisibility Property IV:
If a number is a factor of two numbers (N_{1} and N_{2}) then it is also the factor of the sum of the two given number (N_{1} and N_{2}) and also the factor of the difference of the two given numbers (N_{1} and N_{2})
Example Justifying the Property:
1. 8 is a factor of both 48 and 80.
Then 48 + 80 = 128
Now, 128 is divisible by 8 and it gives 16
Again 80 - 48 = 32
32 is also divisible by 8 and gives 4
2. 6 is a factor of both 72 and 84
Then 72 + 84 = 156
156 is divisible by 6
Again 84 - 72 = 12
12 is also divisible by 6
These properties of divisibility are very useful for the learners while solving arithmetical operations.
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