### How do you show your work for the prime factorization of 140?

Divide the number starting from the smallest prime number, which is 2. 140 / 2 = 70 70 / 2 = 35 140 can be divided by 2 twice only Next we repeat with the next prime number, which is 3. 35 is not divisible by 3 so we move on to the next prime number, which is 5 35 / 5 = 7 35 can be divided by 5 once only Next prime number…

### Why do you say the prime factorization instead a prime factorization?

Saying "The" Instead of "A" The prime factorization is used instead of a prime factorization because there is only one correct prime factorization of any given number. Of course, that refers to composite numbers because prime numbers have no prime factorization. The use of the word "a" implies that more than one prime factorization is possible when it's not. The use of the word "the" signifies that only one prime factorization is possible, though there…