Aptitude - Numbers - Discussion

@All.

According to me, the solution is;

3^65 * 6^59 * 7^71=?
The cycle city of 3 is 4=1
The cycle city of 6 is 1=6
The cycle city of 7 is 4=3
1* 6 * 3,
6 * 3 = 18 = 8/2 = 4.

To find unit digit first we should know the periodic value
ex:-for 2

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64 and so on.

Clearly observe that unit digit follows a cyclic form i.e after 4 terms it again repeating. So the period of 2 is 4.

Similarly for 3, 7, 8 also same period 4.

For 0, 1, 5, 6 period is always same as itself irrespective of their powers.

So to find a unit digit find the period of that number then divided the power value by the period.

ex: 3^65 period for 3 is 4.

Divide 65 by 4 we get reminder 1.
Now unit digit is 3^1 = 3.
6^59 =6.
7^71 =period for 7 is 4.

Divide 71 by 4 we get remainder 3
7^3 =343 => 3(consider unit digit).
So answer is 3*6*3 = 54 => 4 (unit digit is 4).

@All.

Any number to the power of 6 gives unit digit as 6. Right?

I think the answer is 1.

Can you please explain step by step how 6^59=6?

How it comes 6 power of 59 which equals to 6.

Please explain this.

Unit digit of 7^71wxplantion:

7^7=49 in dis unit digit is 9
Then 7 multiplied by 49 leaves unit digit as 3,
Then 7 multiplied again gives 1,
Again 7 multiplied gives 7.

Repaet d order like : 9,3,1,7,9,3,1,7,9,3,1,7
In the order, 11th place gives 1 which would be identical to 7^71.
Ex: lf it's 7^ 72 then the unit place would be 7.

Thanks @Jyothi.

Thanks @Jyothi.

How 6^59 is only 6?