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107. 252 can be expressed as a product of primes as:

A. [tex]2 \times 2 \times 3 \times 3 \times 7[/tex]

B. [tex]2 \times 2 \times 2 \times 3 \times 7[/tex]

C. [tex]3 \times 3 \times 3 \times 3 \times 7[/tex]

D. [tex]2 \times 3 \times 3 \times 3 \times 7[/tex]


Sagot :

Let's identify the prime factorization of the number 252 by breaking it down step by step:

1. Initial division by the smallest prime (2):
- [tex]\( 252 \div 2 = 126 \)[/tex]
- We get our first factor [tex]\( 2 \)[/tex].

2. Continue division by 2:
- [tex]\( 126 \div 2 = 63 \)[/tex]
- We get another factor [tex]\( 2 \)[/tex].

At this point, we cannot divide further by 2 since 63 is not divisible by 2.

3. Division by the next smallest prime (3):
- [tex]\( 63 \div 3 = 21 \)[/tex]
- We get a factor [tex]\( 3 \)[/tex].

4. Continue division by 3:
- [tex]\( 21 \div 3 = 7 \)[/tex]
- We get another factor [tex]\( 3 \)[/tex].

Now, the remaining number is 7, which is already a prime number.

So, the complete prime factorization of 252 is:
[tex]\[ 2 \times 2 \times 3 \times 3 \times 7 \][/tex]

Now, let's compare this prime factorization with the given options:

- Option A: [tex]\( 2 \times 2 \times 3 \times 3 \times 7 \)[/tex]
- Option B: [tex]\( 2 \times 2 \times 2 \times 3 \times 7 \)[/tex]
- Option C: [tex]\( 3 \times 3 \times 3 \times 3 \times 7 \)[/tex]
- Option D: [tex]\( 2 \times 3 \times 3 \times 3 \times 7 \)[/tex]

From the comparisons, we can see that the correct prime factorization matches option A.

Therefore, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
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