Question

explain why 5×11×17+17 is a composite no. while 7×6×3×5+5 is not a composite no​

Answer 1

Second one is just for confusion, both are composite!

Consider the number  5 × 11 × 17 + 17.

We may remember the converse of distributive law.

a × (b + c) = ab + ac      ⇒      ab + ac = a × (b + c)

So,

    5 × 11 × 17 + 17

⇒  17 (5 × 11 + 1)

No need to simplify  5 × 11 + 1,  here we got  5 × 11 × 17 + 17  as product of two positive integers, 17 and 5 × 11 + 1, and also  5 × 11 + 1 ≠ 1.

Hence proved that  5 × 11 × 17 + 17  is a composite number.

Consider the number  7 × 6 × 3 × 5 + 5.  Who said this is not a composite number?!

     7 × 6 × 3 × 5 + 5

⇒  5(7 × 6 × 3 + 1)

Seems that  7 × 6 × 3 × 5 + 5  can be written as product of two positive integers, 5 and 7 × 6 × 3 + 1, and also  7 × 6 × 3 + 1 ≠ 1.

Hence proved that  7 × 6 × 3 × 5 + 5  is also a composite number.