**Hint:** Arrange the numbers in either ascending or descending order to find the greatest and the smallest number.

**Complete step-by-step answer:**

Given numbers are 4536, 4892, 4370, 4452

Arranging the numbers in decreasing order, we get:

Decreasing order means to arrange them from largest to smallest.

\[4892{\text{ }} > {\text{ }}4536{\text{ }} > {\text{ }}4452{\text{ }} > {\text{ }}4370\]

**Therefore the greatest number is 4892 and the smallest number is 4370.**

**Note:** To find the greatest and the smallest number arrange the numbers in either increasing or decreasing order first. Since all the numbers given consist of four digits starting with 4, we check for the number in the hundreds place. Since \[8 > 5 > 4 > 3,\] we get \[4892{\text{ }} > {\text{ }}4536{\text{ }} > {\text{ }}4452{\text{ }} > {\text{ }}4370\]