Express each number as a product of its prime factors:(i) 140(ii) 5005

(i) 140

1. Divide 140 by the smallest prime number, which is 2: 140 ÷ 2 = 70

2. Divide 70 by 2 again: 70 ÷ 2 = 35

3. 35 is not divisible by 2, so move to the next smallest prime number, which is 5: 35 ÷ 5 = 7

4. 7 is a prime number.

So, the prime factorization of 140 is: 140 = 2 × 2 × 5 × 7

(ii) 5005

1. Divide 5005 by the smallest prime number, which is 5: 5005 ÷ 5 = 1001

2. 1001 is not divisible by 2, 3, or 5. Try the next smallest prime number, which is 7: 1001 ÷ 7 = 143

3. 143 is not divisible by 2, 3, 5, or 7. Try the next smallest prime number, which is 11: 143 ÷ 11 = 13

4. 13 is a prime number.

So, the prime factorization of 5005 is: 5005 = 5 × 7 × 11 × 13