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