Multiple choice

Find the largest number which when divides 47, 35 and 27 leaves the same remainder. Also find the value of the remainder?

  1. 3, 4

  2. 4, 3

  3. 1, 9

  4. 9, 1

  5. 3, 1
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B Correct answer
Explanation

We need the largest number d that divides 47-r, 35-r, 27-r. This is d = HCF(47-35, 35-27) = HCF(12, 8) = 4. Remainder: 47/4 = 11 R 3, 35/4 = 8 R 3, 27/4 = 6 R 3. The number is 4, remainder is 3.

AI explanation

To find the largest number that leaves the same remainder, we use the greatest common divisor method on the differences between the numbers. We calculate the differences as 47 minus 35 equals 12, and 35 minus 27 equals 8. The highest common factor of 12 and 8 is 4, meaning the dividing number is 4. Dividing 47 by 4 gives a remainder of 3, so the remainder is 3; the result is 4 and 3.

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