Question

Greatest number which divides 205 and 425 leaving a
remainder 7

Answer 1

Answer:

Step-by-step explanation:

It is given that the required number when divides 205 and 425, the remainder is 5 in each case, This means that 205−7=198 and 425−7=418 are completely divisible by the required number.

It follows from this that the required number is a common factor of 198 and 418. It is also given that the required number is the largest number satisfying the given property. Therefore, it is the HCF of 198 and 418.

Let us now find the HCF of 198 and 418 by Prime factorization method.

2 × 3 × 3 × 11 = 198

2 × 11 × 19 = 418

Therefore HCF = 2 × 11 = 22