Question

Find the greatest number that will divide 137,182,422 leaving the remainder 2 in each case

Answer 1

let a divide them to leave 2 as remainder in each case, then:
a divides (137-2), (182-2), (422-2), i.e.,
a divides 135, 180 and 420.
So, a = HCF (135, 180, 420).
Hope it helps ◕‿◕

Answer 2

Hey friend, Harish here.

Here is your answer:

Let the greatest number that divides them be x.

So, When we subtract the remainder from the number then, x must divide them perfectly.

So, 137 - 2 = 135 , 182 - 2 = 180 , 422 -2 = 420.As x divides the 135, 180, 420,

Then it must be the HCF of them,

Then,

420 = 180 × 2 + 60

180 = 60 × 3 + 0.

130 = 60 × 2 + 10

60 = 10 × 6 + 0.

10 is the HCF Of them.

Therefore 10 is the greatest number that divides them to leave remainder 2.

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Hope my answer is helful to you.