Question

What is the unit digit in (343)125 x (7777)160
a) 1
b) 3 c) 7
d) 9
다.​

Answer 1

Answer:

0

Step-by-step explanation:

Answer will be obvious zero as the one given unit digit is 0.

Answer 2

Therefore the unit digit in 343¹²⁵ × 7777¹⁶⁰ is '3'. ( Option-b )

Given:

Number = 343¹²⁵ × 7777¹⁶⁰

To find:

The unit digit in 343¹²⁵ × 7777¹⁶⁰

Solution:

The given question can be solved as shown below.

Given that: 343¹²⁵ × 7777¹⁶⁰

We need only the unit's place. So let's take only the units digit.

First, let us analyze the unit place of the number 343¹²⁵.

3¹ = 3

3² = 9

3³ = 27

3⁴ = 81

And the same pattern 3, 9, 7, and 1 repeats for every 4 powers

So 125 = 124 + 1

Where 124 is divisible by 4 and the remainder is '1' when 125 is divided by 4. Hence the unit digit for 3¹ is '3'.

Hence the unit digit in the number 343¹²⁵ is '3'

Now, let us analyze the unit place of the number 7777¹⁶⁰.

7¹ = 7

7² = 49

7³ = 343

7⁴ = 2401

And the same pattern 3, 9, 7, and 1 repeats for every 4 powers

So 160/4 = 40

Where 160 is divisible by 4 and the remainder is '0'. Hence the unit digit for 7⁴ is '1'.

Hence the unit's digit in the number 7777¹⁶⁰ is '1'

The unit digit in the number 343¹²⁵ × 7777¹⁶⁰ is 3 × 1 = 3

Therefore the unit digit in 343¹²⁵ × 7777¹⁶⁰ is '3'.

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