Aptitude - Numbers - Discussion

4^2 = 16, 4^3 = 64. Unit digit = 4, when power is 3 (odd).

Unit digit of any number having odd power remains same as the original number has;here 6374^1793. Power is odd so unit digit will be 4, similarly 625^317 & 341^491 unit digits are 5 and 1 respectively, since power is odd.

So the unit digit of overall expression = (4.5.1) = 20 i.e. 0.

Find unit digit of 1^1+2^2+3^3+4^4+5^5+6^6?

(6374)^1793.

= Here unit digit is 4 then we can write (4)^1793.

As we know that multiple of 4 will be = 4, 16, 64, 256 = Here unit digit is 4 and 6 continuing coming then we have to take 2 nos. which should come 4 and 6 that's why we took.

= (4)^1793.

= 4*(4)^1792 (we can write it).

= 4*(4^2)^896.

Take only unit digit = 4*16 = 4*6 = 24 = 4.

Same as:

Unit digit in (625) 317 = Unit digit in (5) 317 = 5.

Unit digit in (341) 491 = Unit digit in (1) 491 = 1.

Answer:

Required digit = Unit digit in (4 x 5 x 1) = 0.

Follow this Rule.

Unit Digit of Base, Powers, Unit digit of 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)^1793x(625)^317x(341)^491)}.

= (6374)^1793 unit digit is 4.

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

Take the remainder to 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) same digit as the unit digit.

So we get (341)^(491) = 1.

Finally (4*5*1) = 20.

Thus unit digit is 0 = Answer.

(209*144) ^2+ (209*209) + (209*144) + (144*144) =?

Please tell me.

@Hemanth.

Your explanation was clear and good. Thanks!

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.

896 * 2 = 1792.....?

Thank you @Seema.

Thank you @Seema.