Question

3. Find the largest number which divides 414 and 608 leaving
remainder 6 and 8 respectively.​

Answer 1

Answer:

24 is your correct answer

Step-by-step explanation:

I hope this will help you

Answer 2

The required number is 24.

Given,

Number 1 = 414

Number 2 = 608

To Find,

The largest number that divides the given numbers leaving the remainder of 6 and 8 respectively =?

Solution,

Let the largest number that divides the given numbers leaving the remainder of 6 and 8 respectively be x

If we subtract the remainder from both numbers then both numbers are divisible by x

Number 1 = 414 - 6 = 408

Number 2 = 608 - 8 = 600

By factorization of 408 and 600, we get

408 = 2 x 2 x 2 x 3 x 17

600 = 2 x 2 x 2 x 3 x 5 x 5

The highest common factor = 2 x 2 x 2 x 3 = 24

The HCF of 408 and 600 = 24

Hence, the largest number that divides 414 and 608 leaving

remainder 6 and 8 respectively is 24