The H.C.F. and L.C.M. of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1: 4, then the larger of the two numbers is

H.C.F. Property: The H.C.F. is always a factor of the L.C.M. (Here, 21 is a factor of 84).Ratio Property: If the ratio of two numbers is a:b and their H.C.F. is x, then the numbers are ax and bx. In this problem, since x (the H.C.F.) was found to be 21, the numbers are 1(21) and 4(21).Sanity Check: Always ensure the H.C.F. you calculate is actually the highest common factor of the two resulting numbers. H.C.F. of 21 and 84 is indeed 21.