Question

Find the greatest number that will divide 55,75and 113 leaving the remainders 7,3 and 5 respectively solved

Answer 1

"greatest number that will divide".....here please notice that the question asks for a for a factor which will be greatest (or better to say: highest) on the remainder being subtracted from the the given numbers
to solve this, first of all subtract the given remainders from their given respective terms:
55 - 7 = 48
75 - 3 = 72
113 - 5 = 108
now the new numbers we have are:
48,72and108
as the question says, we now need to find the HCF of these numbers:
48=2×2×2×2×3
72=2×2×2×3×3
108=2×2×3×3×3
Now taking the common factors,
we have:2×2×3=12
hence, 12 is that greatest number which is required
note: the above method will apply to every question of this kind
note: wherever you find "the greatest number that will divide" these words it means they are asking you to find the HCF(highest common factor)

^o^ hope this helps!!!