75421 ÷ 2 = 37710 R1
Alright, let's work through the division of 75421 by 2 step by step.

Step 1:
2 goes into 7 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 6 from 7 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 2

Step 2:
2 goes into 15 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 37
Subtract 14 from 15 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 2

Step 3:
2 goes into 14 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 377
Subtract 14 from 14 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 2

Step 4:
2 goes into 2 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 3771
Subtract 2 from 2 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 2

Step 5:
2 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 37710
Subtract 0 from 1 to get 1.

The final result is 37710 with a remainder of 1.