Multiple choice

When 78, 94 and 110 are divided by a number, leaves remainder 3, 4 and 5 respectively. Find the number.

  1. 13

  2. 15

  3. 17

  4. 20
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B Correct answer
Explanation

The number must divide (78-3)=75, (94-4)=90, and (110-5)=105. The HCF of 75, 90, and 105 is 15.

AI explanation

Subtract the respective remainders from the numbers to get 75, 90, and 105. The required number must perfectly divide these differences, meaning it is their highest common factor. Prime factorization shows 75 = 3 * 5^2, 90 = 2 * 3^2 * 5, and 105 = 3 * 5 * 7. The highest common factor is 3 * 5, which equals 15. The number is 15.

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