13. What is the prime factorization of 140?

A. [tex]$2 \times 2 \times 5 \times 7$[/tex]

B. [tex]$4 \times 5 \times 7$[/tex]

C. [tex]$2 \times 3 \times 5 \times 7$[/tex]

D. [tex]$5 \times 5 \times 7$[/tex]



Answer :

To determine the prime factorization of 140, we need to break it down into prime numbers, which are numbers greater than 1 and have no divisors other than 1 and themselves.

Here are the steps to find the prime factorization of 140:

1. Start with the smallest prime number, which is 2.
- 140 is even, so it is divisible by 2.
- 140 ÷ 2 = 70
- Write this as [tex]\( 140 = 2 \times 70 \)[/tex].

2. Continue dividing by 2.
- 70 is still even, so it is divisible by 2.
- 70 ÷ 2 = 35
- Now we have [tex]\( 140 = 2 \times 2 \times 35 \)[/tex].

3. Move to the next prime number, which is 3.
- 35 is not divisible by 3 (since the sum of the digits, 3+5=8, is not divisible by 3).

4. Move to the next prime number, which is 5.
- 35 ends in 5, which means it is divisible by 5.
- 35 ÷ 5 = 7
- Now we have [tex]\( 140 = 2 \times 2 \times 5 \times 7 \)[/tex].

5. 7 is a prime number:
- We have reached the number 7, which is a prime number.

So the prime factorization of 140 is [tex]\( 2 \times 2 \times 5 \times 7 \)[/tex].

Therefore, the correct answer is:

A. [tex]\( 2 \times 2 \times 5 \times 7 \)[/tex]