What is the greatest number that divides 37 50 and 123 leaving remainders 1 2 and 3 respectively*?

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• Correct Answer: D

  Solution :

       \[37-1=36,50-2=48,\]       \[123-3=120\] HCF of 36, 48 and 120 = 12 \[\therefore \]Required number = 12.

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Page 2

• Correct Answer: A

  Solution :

      15                               

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Page 3

• Correct Answer: C

  Solution :

      They can all be divided evenly by 3

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Page 4

• Correct Answer: B

  Solution :

      1

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Page 5

• Correct Answer: C

  Solution :

      The smallest 4-digit = 1000 Now L.C.M of 12, 15, 20 and 35
  
  L.C.M  \[=2\times 2\times 3\times 5\times 7=420\] We divide 1000 by 420
  
  \[\therefore \]The least 4-digit number that is exactly divisible by 12 15 20 and 35 = 1000 + (420 - 160)                                 = 1000 + 260 = 1.260

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Page 6

• Correct Answer: A

  Solution :

      (11, 111)         

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Question 9 Using Euclid's division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.

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practice

The greatest number that will divide 37, 50, 123 leaving remainder 1, 2 and 3 respectively is $$37-1=36, 50-2=48$$
$$123-3=120$$
HCF of 36, 48 and $$120=12$$
$$\therefore$$ required number $$=12$$.