Question

m and n are any two natural number show that the product of 2power m and 3 power n not end o or 5​

Answer 1

Correct question:

m and n are two natural numbers. Show that the product of 2^m and 3^n can not end with 0 or 5.

Solution:

Conditions necessary for 2^m × 3^n to end with a 0 or 5:

• The most efficient and easy condition is that 5 must be a factor of 2^m × 3^n. But that can never happen, as no natural number can be found such that when it is raise to 2 or 3 either, results in multiple of 5.

For the above condition to satisfy, one of the digits of 2^m × 3^n must be divisible by 5. But that is not possible.

Thus, 2^m × 3^n can never end with 0 or 5.