Lesson: Units Digit of Large Powers

Comment on Units Digit of Large Powers

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.
gmat-admin's picture

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
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?
gmat-admin's picture

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

Cheers,
Brent

ari.banerjee's picture

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
gmat-admin's picture

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

Cheers,
Brent

Add a comment

Have a question about this video?

Post your question in the Comment section below, and I’ll answer it as fast as humanly possible.

Tweet about the course!

If you're enjoying my video course, help spread the word on Twitter.

Study Guide

The step-by-step Study Guide will help direct your studies and ensure that you cover everything that the GMAT tests.

Free “Question of the Day” emails!