Aptitude - Numbers - Discussion

Why we take power of 7 is only 4?

Any other easy method?

Because this is shortcut for cyclic these types of some e.g.

1, 5, 6 = 0.

4, 9 = 2.

2, 3, 7, 8 = 4.

Rule 1. When remainder is 0 and no. At unit place is even no. Answer is always 6.

Rule 2. When remainder is 0 and no. At unit place is odd and is always 1.

(6^4)^14x6^3 = 1x6 then how come (7^4)^17x7^3 = 1x3.

I don't know how to calculate the unit digit can you explain?

How you will say 3^4=1? I'm get confused can you explain me?

I did not get the answer how can I calculate the unit number please explain me anyone.

How 6^59=6?

Unit digit in 34 = 1 unit digit in (34)16 = 1.

Unit digit in 365 = unit digit in [(34) 16 x 3 ] = (1 x 3) = 3.

Unit digit in 659 = 6.

Unit digit in 74 unit digit in (74) 17 is 1.

Unit digit in 771 = unit digit in [(74) 17 x 73] = (1 x 3) = 3.

Required digit = unit digit in (3 x 6 x 3) = 4.

How the unit digits are find? Please explain clearly.

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

Please explain this.

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).