Circle the greatest integer in each of the following groups.
$
  1){\text{ - 10,6,5, - 11, - 3}} \\
  {\text{2) - 36, - 43, - 29, - 108}} \\
  {\text{3) - 14, - 16, - 1,0,3}} \\
  {\text{4) - 5,0,163,10, - 7}} \\
$

Hint: Integers are the whole-valued numbers which can be either positive or negative. Also, remember that zero is also an integer. Here we will arrange given numbers in ascending order and accordingly will find the greatest integer amongst it.

Complete step-by-step answer:
Remember when you arrange the given integers in the ascending order, negative numbers with the least value are greater among the two.
For E.g. $( - 1) > ( - 100)$
$1.){\text{ - 10,6,5, - 11, - 3}}$
Arrange the above numbers in the ascending order.
$ \Rightarrow - 11, - 10, - 3,5,6$
From the above series- the greatest integer is $6$
Similarly –
${\text{2) - 36, - 43, - 29, - 108}}$
Arrange the above numbers in the ascending order.
$ \Rightarrow - 108, - 43, - 36, - 29$
From the above series- the greatest integer is $( - 29)$
${\text{3) - 14, - 16, - 1,0,3}}$
Arrange the above numbers in the ascending order.
$ \Rightarrow - 16, - 14, - 1,0,3$
From the above series- the greatest integer is $(3)$
${\text{4) - 5,0,163,10, - 7}}$
Arrange the above numbers in the ascending order.
$ \Rightarrow - 7, - 5,0,10,163$
From the above series- the greatest integer is $163$

Note: Know the concepts of the whole numbers, integers, natural numbers, prime numbers, the composite numbers, Rational and irrational numbers. Also, know the difference and correlation among them.