Question

Find the units digit of the expression 4137^743.

Answer 1

The pattern followed by the units digit of multiples of 7 is 7, 9, 3, 1, 7, 9, 3, 1.............

So, the units digit get repeated after every fourth power.

Now, 743 = 740 + 3

= 4 × 185 + 3

So, the units digit for 740^th power will be 1.

For 741^th power, it will be 7.

For 724^th power, it will be 9.

For 743^th power, it will be 3.

Thus, the units digit of the number 4137⁷⁴³ will be 3.