# Lesson: Units Digit of Large Powers

## Comment on Units Digit of Large Powers

### Brent,

Brent,

Could you elaborate on more complicated cycles? (n > 3) I'm still confused on how to find the units digit in those situations after I find the cycle and cycle length. ### Sure thing.

Sure thing.
Let's try the units digit of 7^33

First find the pattern AND the cycle:
7^1 = 7
7^2 = 49
7^3 = --3
7^4 = --1
7^5 = --7
7^6 = --9
7^7 = --3
7^8 = --1
.
.
.
So, the CYCLE = 4

Now focus on the MULTIPLES OF 4 (the cycle)
7^4 = ---1
7^8 = ---1
7^12 = ---1
etc

We want the units digit of 7^33
Since 32 is a multiple of 4, we know that 7^32 = ---1
Since the cycle is 7, 9, 3, 1, 7, 9, 3, 1, etc, we know that the NEXT POWER, 7^33, has units digit 7

Does that help?

Cheers,
Brent

### sir in questions like 234^121

sir in questions like 234^121
here sir can we make pattern of unit digit(by finding cycle) of 4^121 rather than 234^121 since we are interested only in unit digit? ### Yes, that's correct. The

Yes, that's correct. The units digit of 4^121 will be the same as the units digit of 234^121.

Cheers,
Brent ### Hi Brent,

Hi Brent,

Is it safe to assume that the cycle ends as soon as you get 1?

Because any no: multiplied by 1 will repeat that units digit?

So I start looking for pattern and as soon as I reach 1 i count the no:?

Thank you,
Ari Banerjee ### Yes, that rule will work for

Yes, that rule will work for powers of integers ending in 1, 3, 7 and 9

Cheers,
Brent