Question

find the remainder when 2^24 is divided by 35​

Answer 1

Let’s start by evaluating the pattern of the units digits of 3^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 3. When writing out the pattern, notice that we are ONLY concerned with the units digit of 3 raised to each power.

3^1 = 3

3^2 = 9

3^3 = 7

3^4 = 1

3^5 = 3

The pattern of the units digit of powers of 3 repeats every 4 exponents. The pattern is 3–9–7–1. In this pattern, all positive exponents that are multiples of 4 will produce a 1 as their units digit. Thus:

3^24 has a units digit of 1.

Finally, since the remainder is 1 when 1 is divided by 5, the remainder is 1 when 3^24 is divided by 5.

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