Express each number as a product of its prime factors: (i) 140

Step 1: Start with the smallest prime factor

To find the prime factors of 140, we start by dividing it by the smallest prime number, which is 2. Since 140 is an even number, it is divisible by 2.

Step 2: Continue dividing by 2

The result from the previous step is 70, which is also an even number. So, we can divide it by 2 again.

Step 3: Divide by the next prime factor

Now we have 35. Since 35 is not divisible by 2 (it's odd) and not divisible by 3 (sum of digits $3+5=8$, not divisible by 3), we try the next prime number, which is 5. 35 is divisible by 5.

Step 4: Identify the final prime factor

The number we have now is 7, which is a prime number itself. So, we divide 7 by 7, which gives us 1. We stop when we reach 1.

Step 5: Write the prime factorization

The prime factors we found are 2, 2, 5, and 7. We write these as a product to express 140 in its prime factorization form. We can also write $2 \times 2$ as $2^2$.

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