Question

find the greatest number will divided by 180,420 and leaving remainder 2 ,2


please explain​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

180 = 60 × 3 + 0. 60 = 10 × 6 + 0. 10 is the HCF Of them. Therefore 10 is the greatest number that divides them to leave remainder 2

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.

So the correct answer is 15.

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