19742 ÷ 4 = 4935 R2
Alright, let's work through the division of 19742 by 4 step by step.

Step 1:
4 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 4

Step 2:
4 goes into 19 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 16 from 19 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 4

Step 3:
4 goes into 37 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 49
Subtract 36 from 37 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 4

Step 4:
4 goes into 14 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 493
Subtract 12 from 14 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 4

Step 5:
4 goes into 22 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 4935
Subtract 20 from 22 to get 2.

The final result is 4935 with a remainder of 2.