find the greatest number that will divide 37,74 and 182 leaving 1 ,2 and 3 AS remainders respectively
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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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