Question

find the greatest number that will divide 137 182 and 422 leaving the remainder 2 in each case​

Answer 1

In order to make 137, 182 and 422 completely divisible by the greatest number , we need to subtract 2 from each term, so

137-2 = 135, 182-2 = 180 and 422-2 = 420

Now HCF of  135, 180 and 420 is

135 = 3×3×3×5

180 = 2×2×3×3×5

420 = 2×2×3×5×7

Hence HCF of  135, 180 and 420 is 3×5 = 15

Hence the greatest number that will divide 137, 182 and 422 leaving the remainder 2 in each case is 15.

Answer 2

Answer:

The greatest number divides $137$, $182$ and $422$ leaving remainder 2 in every case is 15.

Step-by-step explanation:

To find the greatest number divisible by $137$, $182$ and $422$ leaving the remainder two behind.

Firstly,  we have to subtract two from each number.

We get, $137-2=135$

$182-2=180$

$422-2=420$

Now, find the HCF of $135$, $180$ and $420$ :

$135=3*3*3*5$

$180=2*2*3*3*5$

$420=2*2*3*5*7$

So the highest common factor of  $135$, $180$ and $420$ is $3*5=15$

Therefore, greatest number divides  $137$, $182$ and $422$  equals to 15 leaving remainder two.