Question

Find the largest number which divides 70 and 125, leaving remainders 5 and 8 respectively is:

Answer 1

Hint: Subtracting the remainder from the given numbers and finding the highest common factor gives the greatest number. That gives us the largest number. We have to subtract because above it was mentioned that the number divides the given number and leaves a remainder that means remainder is subtracted to get the number which is divisible by the largest number.

Complete step-by-step solution -
 Let us consider the number 70 first,
Here it was given that 70 when divided by the greatest number leaves the remainder as 5.
Similarly the number 125 when divided by the greatest number leaves the remainder as 8.
Now Considering 70 again.
The greatest number divides 70 and leaves the remainder as 5, that means we have to subtract 5 from 70.
\[70-5=65\].
Now writing the factors for 65 we get,
\[65=13\times 5\]
The greatest number divides 125 and leaves the remainder as 8, that means we have to subtract 8 from 125.
\[125-8=117\].
Now writing the factors for 117 we get,
\[117=3\times 3\times 13\].
To find the greatest number that divides the 2 numbers, we have to find H.C.F (Highest common factor).
\[65=13\times 5\].
\[117=3\times 3\times 13\].
H.C.F of 70 and 125 is \[13\].
Therefore the greatest number that divides 70 and 125 by leaving remainder 5 and 8 is 13.

Note: This is a direct problem with finding the greatest number by writing the factors. The basic step here is to subtract the remainder and then find the greatest number. Highest common factor gives the greatest number that divides the given number.