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]
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]
