Question

Find the unit digit in the product (4387)^{245} (624)^{72} x (23)^{13} 1 2 5 6

Answer 1

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Answer 2

Unit digit in the product is The product of unit digits in individual terms.

So, To find the unit digit in (4387)^{245} × (624)^{72} × (23)^{13}, We need to find unit digits individually and Multiply them over.

So, 4387^245

Unit digit is 7

It is powered to 245.

We know that, Unit digits of 7 repeats themselves after 4 time. That is, 7^1 has the same unit digit as 7^4n + 1

So, 7^245 = 7^244+ 1 = 7^4(61)+1

Unit digit = 7^1 = 7.

Now, (624)^{72}

Unit digit is 4

It is powered to 72

We know that,

Odd power of 4 yields unit digit 4

Even power of 4 yields unit digit 6.

Here, 4^72 in which 72 is even.

So unit digit is 6.

Now,

23^13

Unit digit is 3

It is powered to 13

We know that, Unit digits of 3 repeats themselves after 4 time. That is, 3^1 has the same unit digit as 3^4n + 1

So, 3^13 = 3^4(3)+1

Unit digit = 3^1 = 3

Unit digit of the product

(4387)^{245} × (624)^{72} × (23)^{13}

= 7 * 6 * 3

= 126.

Unit digit is 6.

Hence, 6 is the required answer!