The last digit of the number obtained by multiplying the numbers 81 × 82 × 83 × 85 × 86 × 87 × 88 × 89 will be
To find the last digit of the number obtained by multiplying several numbers, we only need to consider the last digits of each of those numbers. The last digit of the final product is determined by the last digit of the product of the last digits.
The expression is: 81 × 82 × 83 × 85 × 86 × 87 × 88 × 89.
The last digits of these numbers are: 1, 2, 3, 5, 6, 7, 8, and 9.
We need to find the last digit of the product: 1 × 2 × 3 × 5 × 6 × 7 × 8 × 9.
A key shortcut in these problems is to look for the presence of the digits 2 and 5. In this multiplication, we have both a 2 (from 82) and a 5 (from 85).
The product of these two digits is:
2 × 5 = 10
Since the product of the last digits includes a factor of 10, the entire product will have a last digit of 0. Any integer multiplied by 10 will always end in 0.
Therefore, the last digit of the given number is 0.
Reinforce your conceptual grasp with related questions from NIMCET 2018:
It has been reported in recent years that a very large number of seats...
Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.
Start Free Mock Test Series →