Question

unit digit in the product 11*12*13*.....18*19​

Answer 1

Given,

The terms of product are = 11×12×13×.....×18×19

To find,

The unit digit of the product of the given terms.

Solution,

We can either multiply all the numbers starting from 11 upto 19, or we can use the following easy method.

We have to keep in mind that we need the unit digit, so we can simply multiply the unit digits of all the numbers. Because, no addition happens for the unit digits in any multiplication work.

So, unit digit will be

= 1×2×3×4×5×6×7×8×9

= 120×6×7×8×9

Now, the unit digit of a number has come zero. So rest of the unit digits of remaining multiplications will be also zero. (0×any number = 0)

Hence, the unit digit of the given multiplication will be zero.

Answer 2

SOLUTION

TO DETERMINE

The unit digit in the product

$\sf{11 \times 12 \times 13 \times .. \: .. \times 18 \times 19}$

EVALUATION

We have to find the unit digit in the product

$\sf{11 \times 12 \times 13 \times .. \: .. \times 18 \times 19}$

Now

$\sf{11 \times 12 \times 13 \times .. \: .. \times 18 \times 19}$

$\sf{ = 11 \times 12 \times 13 \times .. \times 15 \times .. \times 18 \times 19}$

$\sf{ =(15 \times 18) \times 11 \times 12 \times 13 \times .. \: .. \times 19}$

$\sf{ =270 \times 11 \times 12 \times 13 \times .. \: .. \times 19}$

$\sf{ =10 \times 27 \times 11 \times 12 \times 13 \times .. \: .. \times 19}$

So the number is a multiple of 10

We know that if a number is multiple of 10, then unit digit of the number = 0

So the unit digit in the product $\sf{11 \times 12 \times 13 \times .. \: .. \times 18 \times 19}$ is 0

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