Question

Find the last digit in the product of any 20 consecutive 2 digit odd natural numbers

Answer 1

Solution:

Product of 20 consecutive 2 digit odd natural number

=51×53×55×57×59×61×63×65×67×69×71×73×75×77×79×81×83×85×87×89×91

→→ Last digit in the product of any 20 consecutive 2 digit odd natural numbers

 = Unit digit in the product of ( 1 × 3×5×7×9×1×3×5×7×9×1×3×5×7×9×1×3×5×7×9)

=$(945)^4$

As Fourth power of number 5 always has unit digit equal to 5.

So,   Last digit in the product of any 20 consecutive 2 digit odd natural numbers= 5