Question : Find the greatest number that will divide 49, 147, and 322 to leave the same remainder in each case.
Option 1: 9
Option 2: 5
Option 3: 7
Option 4: 8
Correct Answer: 7
Solution :
When two numbers are divided by another number and have the same remainder, their difference must produce a remainder of zero. Use this concept to solve the question.
According to the question,
The differences will be,
⇒ 147 – 49 = 98
⇒ 322 – 147 = 175
⇒ 322 – 49 = 273
The set of numbers {98, 175, 273}
Now HCF of {98, 175, 273}
⇒ 98 = 7 × 7 × 2
⇒ 175 = 5 × 5 × 7
⇒ 273 = 13 × 7 × 3
The HCF of {98, 175, 273} is 7
Hence, the correct answer is 7.
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