It is a 5 digit no. ,palindrome,divisible by 4,10 digit is cube root of 1 digit,product of 100 digit and 1 digit is 54 ,sum of hundred and ones digit is 15.what is the number?

1039newes123cort

To find the five-digit number that meets all of the given conditions, we need to go step by step.

Condition 1: The number is a palindrome.
A palindrome number is the same when read backward and forward. Since the number is a five-digit palindrome, it must have the following structure: ABCBA, where A, B, and C represent digits.

Condition 2: The number is divisible by 4.
For a number to be divisible by 4, the last two digits must form a number that is divisible by 4. Looking at the palindrome structure, the last two digits are BA. So, BA must be divisible by 4.

Condition 3: The tens digit is the cube root of the units digit.
Let's assign D as the units digit and E as the tens digit. According to the condition, E^3 = D.

Condition 4: The product of the hundreds digit and the ones digit is 54.
If we assign F as the hundreds digit, then F * D = 54.

Condition 5: The sum of the hundreds and ones digit is 15.
So, F + D = 15.

Let's summarize the information we have so far:
A B C B A (The number structure)
E^3 = D (The tens digit is the cube root of the units digit)
F * D = 54 (The product of the hundreds digit and the ones digit is 54)
F + D = 15 (The sum of the hundreds and ones digit is 15)

Now, let's solve the equations to find a possible solution.

From equation 3 (E^3 = D), the possible values for E are 2 (2^3=8), and 3 (3^3=27). Since the number is a palindrome, we can assume E=B.

From equation 4 (F * D = 54), the possible values for F are 2 (2 * D = 54, D = 27), and 6 (6 * D = 54, D = 9).

From equation 5 (F + D = 15), we can combine the possible values of F and D to find the final possible pairs: (2, 13) and (6, 9).

Using the possible pairs, we can construct the possible numbers:
21312
69396

Let's check which number satisfies the condition of being divisible by 4. Since the number must end with BA and be divisible by 4, the only possible solution is 69396.

Therefore, the five-digit number that meets all the given conditions is 69396.