Find the greatest number that will divide that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Question

Find the greatest number that will divide that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Medium

Solution

Verified by GMS

Given numbers are $43, 91$ and $183 .$
Subtract smallest number from both the highest numbers.

we have three cases :

$183 > 43$ ; $183 > 91$ and $91 > 43$

$183 - 43 = 140$
$183 - 91 = 92$ and
$91 - 43 = 48$

Now , we have three new numbers : $140, 48$ and $92$

For HCF of $140, 48$ and $92$ using prime factorization method, we get
HCF $(140, 48$ and $92) = 4$

the highest number that divide $183, 91$ and $43$ and leave the same remainder is $4 .$

Getting Info...