Question

A number,being successively divided by 5, 7 and 11 leaves 3,1,2 remainders respectively.find the remainder if the same number is divided by 385.

Answer 1

so , the remainder is 120/385 . .

Answer 2

Answer:

The remainder will be 78, if if the same given number is divided by 385.

Step-by-step explanation:

• Let the number be X.

• Hence, X being successively divided by 5, 7 and 11 leaves 3, 1, 2 remainders respectively.

• Let the quotient be A when divided by 11.

• As, X being successively divided by 5, 7 and 11 leaves 3, 1, 2 remainders respectively.

Hence, we can write:

X = 5( 7 ( 11A + 2) + 1) + 3

  = 5 ( 77A + 15) + 3

  = 385A + 75 + 3

  = 385A + 78

If we put A = 1,2,3,..... any whole number,

• We get the final number 78 more than a multiple of 385. Hence, if the number is divided by 385,

• so, the remainder will be 78, if if the same number is divided by 385.

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