Divisibility Test IV
Number Theory
Level
1
A four digit number is the same if you read it forwards or backwards. The number is surely divisible by -
Details - The number 1234 read forwards is 1234 and read backwards is 4321.
11
9
2
10
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1 solution
Here the given number is a 4 digit palindrome . We can write it in the form a b b a
We can also write the number as 1 0 0 0 a + 1 0 0 b + 1 0 b + a
⇒ 1 0 0 1 a + 1 1 0 b
⇒ 1 1 ( 9 1 a + 1 0 b )
⇒ 1 1 k where k is an integer
Hence all the 4 digit palindromes are divisible by 1 1