Question
Download Solution PDFFind the greatest number that will divide 49, 147 and 322 to leave the same remainder in each case
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The greatest number that will divide 49, 147 and 322 to leave the same remainder in each case
Concept used:
We must now identify differences between the provided numbers.
When two numbers are divided by another number and have the same remaining, their difference must produce a remainder of zero.
Calculations:
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
∴ The same remainder in each case is 7.
Last updated on Jul 19, 2025
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