Multiple choice

If the last divisor is 75 and the quotients are 3, 1, 1 and 3, respectively, in finding the HCF of two numbers by the method of division, then those two numbers are

  1. 500, 1875

  2. 425, 1675

  3. 525, 1875

  4. 525, 1575

  5. None of these
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C Correct answer
Explanation

Using the division method for HCF in reverse: Last divisor = 75, last quotient = 3. Number = 75*3 + 0 = 225. Previous divisor = 225, quotient = 1. Number = 225*1 + 75 = 300. Previous divisor = 300, quotient = 1. Number = 300*1 + 225 = 525. Previous divisor = 525, quotient = 3. Number = 525*3 + 300 = 1875. The numbers are 525 and 1875.

AI explanation

Working backwards from the last divisor of 75 using Euclidean division, the dividend for the last step is 75 * 3 + 0 = 225. The previous dividend becomes 225 * 1 + 75 = 300. The next dividend is 300 * 1 + 225 = 525. The final first number is 525 * 3 + 300 = 1875. The two numbers are 525 and 1875.

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