1.3 Multiply by breaking the second number into its prime factors: $$ 250 imes 240 $$

Question

1.3 Multiply by breaking the second number into its prime factors: $$ 250 	imes 240 $$

UpStudy AI · Accepted Answer

We start by writing the second number in its prime factors:

$$
240 = 2 \times 2 \times 2 \times 2 \times 3 \times 5 = 2^4 \times 3 \times 5.
$$

Now, rewrite the multiplication:

$$
250 \times 240 = 250 \times \left(2^4 \times 3 \times 5\right).
$$

Next, note that $$ 250 $$ can be written as:

$$
250 = 2 \times 125 = 2 \times 5^3.
$$

Thus, the multiplication becomes:

$$
250 \times 240 = \left(2 \times 5^3\right) \times \left(2^4 \times 3 \times 5\right).
$$

Combine the like bases:

- For the factor 2:

$$
2 \times 2^4 = 2^{1+4} = 2^5.
$$

- For the factor 5:

$$
5^3 \times 5 = 5^{3+1} = 5^4.
$$

So the expression simplifies to:

$$
250 \times 240 = 2^5 \times 3 \times 5^4.
$$

Now, calculate each part:

- $$2^5 = 32$$,
- $$5^4 = 625$$.

Thus, we have:

$$
250 \times 240 = 32 \times 3 \times 625.
$$

Compute the product step by step:

1. Multiply $$32 \times 3$$:

$$
32 \times 3 = 96.
$$

2. Multiply the result by $$625$$:

$$
96 \times 625 = 60000.
$$

So, the final product is:

$$
250 \times 240 = 60000.
$$
$$ 250 \times 240 = 60,000 $$

1.3 Multiply by breaking the second number into its prime factors: \( 250 \times 240 \)