PREVIOUSLY ASKED IN:
PSC Miscellaneous Prelims 2018
Answer
12
Explanation
The problem states that the required greatest number divides 303 and 207 leaving a remainder of 3 in each case. This means if we subtract 3 from the given numbers, the resulting numbers will be exactly divisible by the required greatest number. The numbers are (303 - 3) = 300 and (207 - 3) = 204. The greatest number that divides both is their Highest Common Factor (HCF). The HCF of 300 and 204 is 12. Therefore, 12 is the required number.
Key Points
- > The phrase 'greatest number that divides' indicates finding the HCF.
- > When a remainder is given, subtract it from the numbers first.
- > The exact divisible numbers are 300 and 204.
- > Find the highest common factor of 300 and 204.
- > Both numbers are divisible by 12 (300/12 = 25; 204/12 = 17).
- > Since 25 and 17 are co-prime, 12 is the highest common factor.
Additional Information
LCM/HCF Problem Solving Guide
| Problem Keyword | Operation to Perform |
|---|---|
| Greatest/Largest number | Find HCF |
| Least/Smallest number | Find LCM |
| Leaves same remainder 'R' | Subtract 'R' from all numbers, then find HCF |
| Leaves different remainders | Subtract respective remainders, then find HCF |
Memory Tips
- Option Elimination: You don't always need to calculate the HCF fully. Check the options backwards. Can 300 and 204 be divided by 24? No. By 18? No. By 15? No. By 12? Yes. So 12 is the answer.