Question

(3127)^173 unit place​

Answer 1

Answer:

Units digit of 3127¹⁷³ = 7

Step-by-step explanation:

In this Question, we have actual higher level method to solve, but we definitely can solve it using logic.

Let's see how,

Now,

3127¹ = 3127

3127² = 9,778,129

3127³ = 30,576,209,383

3127⁴ = 95,611,806,740,641

3127⁵ = 298,978,119,677,984,407

3127⁶ = 934,904,580,233,057,240,689

And definitely I am not gonna make you do it upto 173th power, because there will be a billion numbers.

Ok, I did this so that you could understand the pattern of the numbers.

If you observe closely you can find that the units digit goes as 7, 9, 3, 1, and repeat again.........

So, there is a definite pattern and repetition of numbers.

Now, they are a set of 4 numbers that keep repeating,

7, 9, 3, 1

You might ask why,

In multiplication, units digit is not interrupted like the other digits of the number.

3127 has 7 units

then,

3127 × 3127 = considering only units digit

= 7 × 7 = 49, so 9 units digit,

Similarly,

9 × 7 = 63, so 3 units digit

then,

3 × 7 = 21, so 1 units digit

See units digit is never disturbed eventhough, 4, 6, 2 and all become carry overs.

Now, back to our Original Question, after observing.....

Let's say we divide 173 in sets of 4, so we must divide 173 with 4

173 ÷ 4 = 43, and remaider 1,

This means there will be 43 whole sets (of numbers 7, 9, 3, 1) and 1 set with only 1 number.

We know the pattern is 7, 9, 3, 1

So, after repeating it 43 times, the next number will be 7 again right.

See,

7, 9, 3, 1,...(repeating 42 times)(because 1 already wrote a set).......(ends with) 1, (next number after 1 =) 7.

So, in number it will be,

7, 9, 3, 1,...........3, 1, 7.

So,

Units digit of 3127¹⁷³ = 7

Hope it helped and believing you understood it........All the best