Units digit question

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1

<p>What is the units digit of 2^5000?</p>

<p>2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32</p>

<p>The pattern is 2, 4, 8, 6, 2, 4, 8, 6, ...</p>

<p>Now, I divide 5000/4 and get 1250... What do you do when the remainder is zero? How do you know which digit in the sequence 5000 falls on if there is no remainder?</p>

<p>Edit: since the remainder is 0, does that mean that 5000 falls on the 4th number in the pattern, 6?</p>

2

<p>I think it does. Yes, I think that 6 is a correct answer!</p>

3

<p>YES! The trick with pattern questions like this is to count on the RIGHT hand side of the column (if you stack the pattern).</p>

<p>So in this case:</p>

<p>2, 4, 8, 6,
2, 4, 8, 6,
2, 4, 8, 6…</p>

<p>Every term that’s an even multiple of 4 will be 6.</p>

<p>Nice work.</p>