Multiple choice

The greatest number which can divide 309, 814 and 2219 leaving the remainders 3, 4 and 5 respectively is

  1. 16

  2. 17

  3. 18

  4. 19
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number must divide (309-3)=306, (814-4)=810, and (2219-5)=2214. Find the HCF of 306, 810, 2214. 306 = 18*17, 810 = 18*45, 2214 = 18*123. HCF is 18.

AI explanation

Subtract the respective remainders from the given numbers to get the exact divisors, which are 309 minus 3 equals 306, 814 minus 4 equals 810, and 2219 minus 5 equals 2214. The required greatest number is the highest common factor of 306, 810, and 2214. Factoring out 18 from each gives 17, 45, and 123, which share no further common factors. The result is 18.

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