If a number is divisible by both 3 and 5, then it is divisible by 15.
Example 1 :
Check whether 41295 is divisible by 15.
Solution :
We know that if the given number is divisible by both 3 and 5, then it is divisible by 15.
First, check whether the given number is divisible by 3.
Sum of the digits :
4 + 1 + 2 + 9 + 5 = 21
Sum of the digits (21) is a multiple of 3.
So, the given number is divisible by 3.
Now, check whether the given number is divisible by 5.
In the given number 41295, the digit in one's place is 5.
So, the number 41295 is divisible by 5.
Now, it is clear that the given number 41295 is divisible by both 3 and 5.
Therefore, the number 41295 is divisible by 15.
Example 2 :
Check whether 2900 is divisible by 15.
Solution :
We know that if the given number is divisible by both 3 and 5, then it is divisible by 15.
First, check whether the given number is divisible by 3.
Sum of the digits :
2 + 9 + 0 + 0 = 11
Sum of the digits (11) is not a multiple of 3.
So, the given number is not divisible by 3.
Because the given number 2900 is not divisible by 3, it is not divisible by 12.
Example 3 :
Check whether 4350 is divisible by 15 or not.
Solution :
We know that if the given number is divisible by both 3 and 5, then it is divisible by 15.
First, check whether the given number is divisible by 3.
Sum of the digits :
4 + 3 + 5 + 0 = 12
Sum of the digits (12) is a multiple of 3.
So, the given number is divisible by 3.
Now, check whether the given number is divisible by 5.
In the given number 4350, the digit in one's place is 0.
So, the number 4350 is divisible by 5.
Now, it is clear that the given number 4350 is divisible by both 3 and 5.
Therefore, the number 4350 is divisible by 15.
Example 4 :
Which of the following numbers should be multiplied by 25 to make a number divisible by 15 ?
(A) 2, (B) 3, (C) 4
Solution :
2 ⋅ 25 = 50
3 ⋅ 25 = 75
4 ⋅ 25 = 100
In the above calculation, when we multiply 3 by 25, we get 75 which is divisible by both 3 and 5.
Because 75 is divisible by both 3 and 5, it is divisible by 15.
So, option B is correct.
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