What is The Remainder When 8^48 Divided by 10?

1. 8
2. 4
3. 2
4. 6
5. 0

Answer:  D

Explanation:

Given,

When a number is divided by 10, always the unit’s place is the remainder.

So, we need to find the unit’s place of 8^{48}

Concept:

Every digit (0,1,2, 3…9) when raised to a power follows a pattern, i.e., there is a cyclicity in the values of the unit’s digits when raised to powers.

The pattern for 8:

8^1 – 8

8^2 – 64

8^3 – 512

8^4 – 4096

So, if we look at it the unit’s digit pattern for 8 raised to a positive integer is 8, 4, 2 and 6 in that order.

To find the unit’s place, take the power and divide it by 4.

If Rem-1🡪  8^1 – 8

If Rem 2 🡪 8^2 – 4

If Rem 3 🡪 8^3 – 2

If Rem 0 🡪 8^4 – 6

Here the power is 48, and when divided by 4 remainder is 0.

So, it ends with 6.

Hence the answer is D.

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