Three Digit Palindromes

A palindrome is a sequence of characters which reads the same backward or forward.

What is the smallest three digit palindrome number divisible by 18 It has to be divisible by both 9 and 2. As 2 and 9 are co-primes. So it has to be even and sum of digits multiple of 9. So lets start with the smallest even "number 2" as we know 2X2 is palindrome (or if we fail try larger number) 2 + X + 2 = 9 => X = 5. Hence solved with smallest even. So the smallest three digit palindrome number divisible by 18 is 252.

OR

The other way around you can solve it by adding 18 together until you get 252 i.e (smallest three digit palindrome). 18 x 14 = 252

A palindrome is a sequence of characters which reads the same backward or forward.

We know that no palindrome of 18 will be there from 1-99..

Now for 100-199...there will not be any palindrome of 18 since no no. having unit digit as 1 is not divisible by 18.

Now for 200-299...if any palindrome exists then it will be of the form: 2_2.

For it to be divisible by 18, it should be divisible by both 2 and 9...

Since it is divisible by 2 only one condition is left: divisibility by 9.......For the no to be divisible by 9 ,its sum of digits should be divisible by 9...

So let the no be 2(x)2... Now 2+x+2= x+4..

Since x cannot be >10....x can only be 5

Thereby the no is $\boxed{252}$

A palindrome is a word or sentence or number that reads the same forward as it does backward.

SO,

It can never start with 1, since 1 does not come in 18 table.

So we directly come to 200 range, first is 202, if we divide 202, we get 4 as a remainder, Just, take first 2 digits

i.e20 when we divide 20 by 18, we get 2 and the next digit is 2. So we get 22.

But we know 72 is divisible by 18,

so, no. = (18 + 7)2

It is not multiplication, I have written the number itself,

so, no = 252

3 digit number & smallest & divisible by 18. Smallest number we have to go from 100. Its is palindrome, (its like 101,111,121 etc..)

And divisible by so the number ends with even number (2,4,6........)

Smallest number its only in 2_2. 202,212,232,242 does not dividable by 18.

252 is divisible by 18 and palindrome

The number has to be divisible by 9 and 2. Which means an even number divisible by 9. A Palindrome is a number like xyx. Here the number x must appear amongst all the multiples of 9. The smallest such number is 2 (9x8=72). For xyx to be divisible by 9 x+y+x must be divisible by 9. The only number fitting that description is 252.

18 = 2 x 9. Any even number is divisible by 2, and for a number to be divisible by 9, its sum must be a multiple of 9.

If the three digit palindrome starts with 1, then it must end in once, hence it would be odd. This is not divisible by 2.

Next we look at three digit palindromes starting with 2. These are always even, and so next we must check if any numbers are divisible by 9.

2X2 = 9n (where n is a non-negative number, and has to be as small as possible)

If n = 0, 9n = 0, and so X = -4. This is not possible.

If n = 1, 9n = 1, and so X = 5. This works.

Therefore, the smallest three digit palindrome divisible by 18 is 252.

Let the three digits be x, y, x

Since the number is divisible by 18 , then x must be even and 2 x + y = 9 n, n = 1, 2, 3, ....

To get the smallest number, x must equal 2(the smallest even digit), hence y = 5, n = 1

So the number is 252

Three digits. Palindrome. Divisible by 18. This means that it is divisible by 2, and by 9. The sum of the digits will add up to a multiple of 9, and the first and last digits will be even.

Because both the first and last digits will be the same, the sum of the first and last digits will be a multiple of 4. That means the middle number will be a multiple of 9 minus a multiple of 4.

I was too lazy to actually fully explore this property but I didn't need to. My first guess was 252, which was the lowest possible.

If 252 didn't work, I'd have guessed 414, and then 666, and then 828.

Helping You By Telling You That What Is Palindromes. A palindrome is a word or sentence or number that reads the same forward as it does backward.