Question

How will you show that (5x3x2)+(5×3×7)
is a composite number ? Explain.​

Answer 1

Step-by-step explanation:

We know that,

The Fundamental Theorem of Arithmetic (FTA) states that every composite number can be factored uniquely (except for the order of the factors) into a product of powers of prime factors.

So,

If we just put there numbers into products of powers of prime numbers, then we can prove that this number is a composite number.

Now, we have,

(5 × 3 × 2) + (5 × 3 × 7)

Taking (5 × 3) common,

(5 × 3)(2 + 7)

(5 × 3)(9)

(5 × 3 × 9)

(5 × 3 × (3 × 3))

= 5 × 3 × 3 × 3

= 3³ × 5

Here, 3 and 5 are prime numbers.

Hence,

[(5 × 3 × 2) + (5 × 3 × 7)] is a composite number, according to FTA.

Hope it helped and believing you understood it........All the best