Question

Let n be the greatest number that will divide 148, 246 and 623 leaving remainders 4, 6 and 11 respectively. what is the remainder if n is divided by 7?

Answer 1

We know that When a greatest number that divide x,y,z and leaves remainder a,b,c respectively = HCF of (x - a),(y - b),(z - c).

Now,

HCF of (148 - 4),(246 - 6),(623 - 11)

= > HCF of (144, 240,612)

Prime factorization of 144 = 2 * 2 * 2 * 2 * 3 * 3

Prime factorization of 240 = 2 * 2 * 2 * 2 * 3 * 5

Prime factorization of 612 = 2 * 2 * 3 * 3 * 17

HCF(144,240,612) = 2 * 3 * 3 = 12.

Hence, the greatest number is n = 12.

Now,

We have to find the remainder when n is divided by 7.

= > 7)12(1

        7

       ---

        5.

Therefore, the remainder is 5.

Hope this helps!