Find the greatest number that will divide 49, 147 and 322 to leave the same remainder in each case.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 7.
Concept Used:
When two numbers are divided by another number and leaves same remainder their difference must produce a remainder that is equal to zero.
Explanation:
Difference between the numbers
⇒ 147 - 49 = 98
⇒ 322 - 147 = 175
⇒ 322 - 49 = 273
Now, HCF of (98, 175, 273),
⇒ 98 = 7 × 7 × 2
⇒ 175 = 7 × 5 × 5
⇒ 273 = 13 × 7 × 3
The HCF of (98, 175, 273) is 7
Hence the greatest number that will divide 49, 147 and 322 to leave the same remainder in each case is 7.