Example:
Without actual division, check whether 779183 is divisible by 13.
Solution:
Here, we need to use the divisibility rule of 13.
To check the divisibility of a number by any
prime number (other than 2), at
first, we have to find a ‘key number’ for the prime number.
How to find key number ?
To find the ‘key number’ of any prime number,
1)
Multiply it by a number (the least
number) such that the unit digit of the product will be 9.
2)
Then, add 1 to the product. Now, the
sum becomes a multiple of 10.
3) Divide the sum by 10. The quotient will be the ‘key number’.
So, we can find the key number of 13 as follows:
Thus, the key number for 13 is 4.
How to check divisibility ?
We can use the ‘key
number’ to check the divisibility as
shown below:
(Extract the last digit and multiply it by the key number and then add the product)
20 is not divisible by 13.
Hence, the given
number is not divisible by 13.
Note: We can continue the process till we get a
small number.
ALTERNATIVE
METHOD:
We
know that the key number for 13 is 4. Right ?
Let’s
say that 4 is the first key number for 13.
Then, the second key number for 13
= 13 – the first key
number
= 13 – 4 = 9
How
to check divisibility by using the 2nd key number ?
We can use the ‘2nd
key number’ to check the divisibility as shown below:
5 is not divisible by 13.
Hence, the given
number is not divisible by 13.
Note:
1) It is better to use the key number
which is smaller.
2) This rule is applicable for all the prime
numbers except 2.
PROBLEMS
FOR PRACTICE:
1) By using the divisibility rule, check whether the following numbers are
divisible by 13. (use 4 as the key number)
(a) 773318
(b) 1285330
2) By using the divisibility rule, check whether the following numbers are
divisible by 13. (use 9 as the key number)
(a) 1147627
(b) 863172
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