Question

Find the greatest number that will divide 42, 90 and 182 so as to leave the same remainder in each case. .

Answer 1

Answer:

4 is the greatest number that will divide 42, 90 and 182 so as to leave the same remainder in each case.

Step-by-step explanation:

To find : The greatest number that will divide 42, 90 and 182 so as to leave the same remainder in each case.

By the theory - If two numbers give the same remainder when divided by some other number, then their difference must give a remainder of zero when divided by that number:

So, our first step is to find the difference between numbers.

We have here 42 ,90 and 182

So differences are  :

182 - 90 = 92,

182 - 42 = 140,

90 - 42 = 48.

Now, We find the HCF of their differences

i.e, HCF of (48,92,140)

48 = 2 × 2 × 2 × 2 × 3,

92 = 2 × 2 × 23,

140 = 2 × 2 × 5 × 7

HCF = 2 × 2 = 4.

Therefore, 4 is the required number.