Aptitude - Numbers - Discussion

Unit Digit of Base, Powers, Unit digit of the product.

0, 1, 5, 6, any powers, same digit.
3, 7, 9, power exactly divisible by 4, 1.
2, 4, 8 " 6.

So in this problem: {(6374)^1793 x (625)^317 x (341)^491)}.
= (6374)^1793 unit digit is 4.

Apply the above rule: Divide 1793 by 4, we get remainder as 1.

Take the remainder of the power of unit digit's i.e. 4^1.

So we get (6374)^1793 = 4. For (625) ^317 same digit as the unit digit.
So we get (625)^317 = 5. For (341)^(491) the same digit as the unit digit.
So we get (341)^(491) = 1.
Finally (4 * 5 * 1) = 20.

Thus unit digit is 0 = Answer.

Your method is very easy. Thank you @Ramya.

Please give the clarity to solve the problem.

@Seema, you have done a good job.

yes you are good @Seema.

Find the product of the first 8 terms of a 15 number sequence whose 1st, 3rd, 5th numbers are 60, 45 and 30?

Thank you @Seema.

Thank you @Seema.

896 * 2 = 1792.....?

Friends. There is a simple way to get this answer.

Consider the unit digit means the last digit. Here in this question, 4 is the unit digit of 6374 and 5 is the unit digit of 625 and 1 is the unit digit of 341.

We want to find the unit digit. So avoid the other numbers.

So, the next step is a simple method we only using the logic behind the multiplication.

(4)^any odd no = 4.
(4)^any even no = 6.
(5)^any no = 5.
(1) any no =1 what I meant that.

4^1 = 4.
4^2 = 16.
4^3 = 64.

i.e, the unit digit are 4 & 6 and this is repeating. Did you get my point?

So by using this method.

(4) ^1793 * (5) ^317 * (1) ^491 = ?
4 * 5 * 1 = 20.

So the unit digit is 0.

Hope, this help you. Thank you.