1) Find the largest number which exactly divides 70, 80, 105 160.

2) Find the largest number which divides 699, 572, and 445 leaving remainders 6, 5 4.

1) To find the greatest number which exactly divides 70, 80, 105 and 160, we have to find H.C.F. of these numbers as;
$$\begin{gathered} 70 = 2\times 5\times 7 \\ 80 = 2\times 2\times 2\times 2\times 5 \\ 105 = 3\times 5\times 7 \\ 160 = 2\times 2\times 2\times 2\times 2\times 5 \end{gathered}$$
So H.C.F of 70, 80, 105 and 160 = 5
Therefore 5 is the number which exactly divides 70, 80, 105 and 160.

2) As 6 is a remainder in 699
So subtract 6 from 699
This means 699 - 6 = 693 is exactly divisible by the required number.
Similarly subtract 5 from 572 and 4 from 445
So, 572 - 5 = 567 and 445 - 4 = 441 are exactly divisible by the required number.
So, H.C.F. of 693, 567 and 441 is the required number.
Prime factorisation of 693 = $3\times 3\times 7\times 11$
prime factorisation of 567 = $3\times 3\times 3\times 3\times 7$
And prime factorisation of 441 = $3\times 3\times 7\times 7$
So H.C.F of 693, 567 and 441 = $3\times 3\times 7 = 63$
Therefore the required number is 63.