70379 ÷ 7 = 10054 R1
Alright, let's work through the division of 70379 by 7 step by step.

Step 1:
7 goes into 7 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 7 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 7

Step 2:
7 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 0 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 7

Step 3:
7 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 100
Subtract 0 from 3 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 7

Step 4:
7 goes into 37 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 1005
Subtract 35 from 37 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: 10054
Subtract 28 from 29 to get 1.

The final result is 10054 with a remainder of 1.