· Test the divisibility of the following numbers by 3: 17244
Answers
Answer:
According to divisibility test of 3, the sum of digits (1 + 7 + 2 + 4 + 4 = 18) is divisible by 3, which means the number 17244 is also divisible by 3.
Step-by-step explanation:
Consider, for simplicity, a 3 digit number 'abc", such as 321.
Suppose that a+b+c is divisible by 3.
Our number, written as 'abc' is actually
100a+10b+c.
For instance, 321 = 100*3+10*2+1.
Let's rewrite 100a+10b+c as 99a+a + 9b+b + c.
99a+a + 9b+b + c = (99a + 9b) + (a + b + c)
The first part is always divisible by 3 since numbers with all nines are always divisible by 3 (9 = 3*3, 99=33*3, 999=333*3 etc).
That the second part (a+b+c) is divisible by 3, is a given.
So, we have a sum of two parts, both of which are divisible by 3. This sum is, therefore, also divisible by three.
Source:
The above proof is from Arihant Bansal, a math writter in the website Quora, if you want to know more please research your question along with that person's name in the Quora website.
Hoping that it helped....
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