7.
Find the greatest number which divides 228, 305 and 382 leaving remainders 3,5 and
7 respectively.​

2 thoughts on “7.<br />Find the greatest number which divides 228, 305 and 382 leaving remainders 3,5 and<br />7 respectively.​”

1. Given :– Find the greatest number which divides 228, 305 and 382 leaving remainders 3,5 and 7 respectively.

   Answer :–

   finding the difference first,

   → (228 – 3) = 225

   → (305 – 5) = 300

   → (382 – 7) = 375 .

   now, prime factors of 225, 310 and 375 are :-

   → 225 = 3 * 3 * 5 * 5

   → 300 = 2 * 2 * 3 * 5 * 5

   → 375 = 3 * 5 * 5 * 5

   finding HCF of difference now,

   → HCF = 3 * 5 * 5 = 75 .

   Therefore, we can conclude that, the the greatest number which divides 228, 305 and 382 leaving remainders 3,5 and 7 respectively will be 75 .

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   वह छोटी से छोटी संख्या बताईये जिसमे 7,9,11 से भाग देने पर 1,2,3 शेष बचे

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2. Answer:

   The question is to find the H.C.F ( G.C.D)

   Subtract the remainders from the respective numbers:

   228-3 = 225

   305-5 = 300

   382-7 = 375

   Now find the hcf of 225,300,375 and it will be the greatest number that divides 228,305 and 382 to leave respective remainders

   225 = 15*15 = 3*3*5*5

   300= 5*60 = 5*5*12= 5*5*3*2*2

   375 = 5*75 = 5*5*5*3

   Hence HCF(GCD) is 5*5*3 = 75 [two 5’s and one 3 is common to all numbers]

   Hence 75 is the greatest number which divides 228,305 and 382 to leave remainders 3,5,7 respectively.

   Hope this helps

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