Question

Show that 3*n will end with a digit 1, 3, 7 or 9
for any natural number n less than or equal to 5.​

Answer 1

Answer:

Answer with explanation:

We have to show that , whether 3 n can end with digit 1 or not for , n=1.

I will prove this using the divisibility property of 3.

A number is divisible by 3, if sum of digits of number is divisible by 3.

Now, write few numbers having unit digit 1, for example

Some two digit numbers are : 11, 21,31,41, 51, 61.

Three digit numbers are : 101, 151, 171, 191

When you look at these numbers , sum of the digits of two digit number are : 11=1 +1=2 , 21=2+1= 3 , 31=3+1= 4 , 51=5+1=6 , 61=6+1=7.

So, 21, 51 is divisible by 3.

Now, add the digits of, 101=1+0+1=2 , 151=1+5+1=7 , 171=1+7+1=9 , 191=1+9+1=11

So, number 151, is divisible by 3.

You , can check for four digit number also, whose unit digit is 1.

Hence, 3 n, can end with digit 1 , for n=1.