Question

find the unit digit 1 ! X 2! X 3! X...
X 100! ?​

Answer 1

Answer:

Here, try to notice this thing-

24*24=576

4*4=16

14*14=196

14*15=210

Here, we find that the unit digit depends on the unit digits of the numbers being multiplied.

ie in 24*24, the unit digit is 4 and 4.

Also, 4*4=16

Now, back on question.

24^100=24*24*24…..100 times

Now,

4*4=16………[24*24]

6*4=24………[576*24]

4*4=16

6*4=24

Here, we see that as we go ahead, the unit digits go like 6, 4, 6, 4.

ie. 24^1→ 4

24^2→ 6

24^3→ 4

24^4→6

Here, the cycle formed is of two {see that 4, 6 repeat after 2 powers}.

Now try to find the unit digit of 24^4 with this concept.

Divide 4 [power] by 2 [cycle].

Find remainder [in this case, it is zero]

If remainder is one, the unit digit is equal to unit digit of 24^1, if it is 0, or we can also say it as 2, the unit digit is equal to 24^2 [here it is 6]

We found the answer[here, it is six, match it with what we found above.]

Back on your question,

24^100

Divide 100 by 2

remainder = 0 or we can say 2

Unit digit of 24^2=6

You found your answer .