Question

What will be the largest number that divides 163 and 243 leaving 3 as remainder

Answer 1

163-3 =160
243-3=240
160= 2*2*2*2*2*5
240 = 2*2*2*2*3*5
HCF = 2^4*5
=80

Answer 2

The largest number that divides 163 and 243 leaving 3 as the remainder is 80.

Given: The numbers 163 and 243

To Find: The largest number divides 163 and 243 leaving 3 as the remainder.

Solution:

• To find the largest number which divides 163 and 243 leaving the remainder 3 in each case, we need to think about HCF.
• Now, it is said that 3 should be left as a remainder, so we need to subtract 3 from both the numbers before finding their HCF.

We are given the numbers 163 and 243. Subtracting 3 in each case we get,

        163 - 3 = 160 and 243 - 3 = 240

So, we shall find the HCF of the numbers 160, and 240.

The prime factorization of 160 and 240 can be given as,

160 = 2 x 2 x 2 x 2 x 2 x 5

240= 2 x 2 x 2 x 2 x 3 x 5

⇒ HCF = 2 x 2 x 2 x 2 x 5

            = 80

Hence, the largest number that divides 163 and 243 leaving 3 as the remainder is 80.

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