96419 ÷ 7 = 13774 R1
We're going to perform division on 96419 with 7 as the divisor.

Step 1:
7 goes into 9 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 9 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 7

Step 2:
7 goes into 26 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 21 from 26 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 7

Step 3:
7 goes into 54 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 137
Subtract 49 from 54 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 7

Step 4:
7 goes into 51 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 1377
Subtract 49 from 51 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 7

Step 5:
7 goes into 29 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 13774
Subtract 28 from 29 to get 1.

The final result is 13774 with a remainder of 1.