What is the greatest number which leaves the same remainder in each case, when divides 265, 580 and 825?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 35.
Concept used:
The greatest number which leaves the same remainder in each case is equal to the HCF of the difference of the numbers
Calculations:
Difference of the numbers = (580 - 265), (825 - 580), (825 - 265)
= 315, 245, 560
Using the factorization method, we get
Factors of 315 = 32 × 5 × 7
Factors of 245 = 5 × 72
Factors of 560 = 24 × 5 × 7
Hence, the HCF of the numbers = Greatest number = 5 × 7 = 35