Lesson: Units Digit of Large Powers

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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

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