What is the General Form of Numbers?
If a two digit number pq needs to represented in general form, then
Divisibility by 9 and 3
If a number X has the sum of its digits divisible by 3 and 9, then the number is divisible by 9 and 3.
For example, let’s see the divisibility of the number 15287 by the number 3.
Let’s see the addition of the digits in the given number
1+5+2+8+7 =23 and the number is not divisible by 3. Therefore, 15287 is not divisible by 3
Let’s see another example of a three digit number 24x which is divisible by 9 and what is the value of x.
The addition of the digits 2+4+x=6+x should be divisible by 9 and this results in the values 6 + x =9 or 18 and since x is a single digit, therefore, 6 + x = 9, x= 3
Reversing the Digits in a number with 2 digits
Lets us assume a number ab in which a is in the tens place and b is in the units place. And then the representing numbers in general form results in ab=10a+b. Reversing the number will result in the form ba=10b+a. After adding the two number, we get :
(10a+b) + (10b+a)=11a+11b=11(a+b)
The given number is a multiple of 11.
Reversing the Digits in a number with 3 digits
The general form of a number of three digits is abc=100a+10b+c. After reversing, the number will be cba=100c+10b+a
- If a>c, the difference between the numbers will be
- Similarly, if c>a, then the difference will result in 99(c-a)
- If a=c then difference is 0
- Find out the value of y if 21y5 is divisible by 9 and y is a number
- Find out the value of z if 31z5 is divisible by 9 and z is a number
- Find out the value of x if 24x is divisible by 3 and x is a digit
- Find out the value of z if 31z5 is divisible by 3 and z is a digit