a)Find the H.C.F. of the smallest composite number and the smallest prime number.

b) . If a = 4q + r then what are the conditions for a and q. What are the values that r can take?

1.

smallest prime number is 2 and smallest composite number is 4.

since 4 = 2*2

HCF of 2 and 4 is 2.

therefore the HCF of smallest prime number and smallest composite number is 2.

2.

if a = 4q+ r.

r can take the values either of 0,1,2,3

and the number a is of the form 4q , or 4q+1, or 4q+2 or 4q+3.

hope this helps you.

cheers!!