Multiple choice

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

  1. 4

  2. 5

  3. 8

  4. 2
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A Correct answer
Explanation

For same remainder r, we have: 43 = d×a + r, 91 = d×b + r, 183 = d×c + r. Taking differences: 91-43 = 48, 183-91 = 92. HCF of 48 and 92 is 4. Verification: 43÷4=10 r3, 91÷4=22 r3, 183÷4=45 r3. Same remainder 3 in each case.

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