what is the prime factorization of 154? 2 × 5 × 13 2 × 5 × 11 2 × 7 × 11 2 × 7 × 13
The correct answer and explanation is:
The correct answer is: 2 × 7 × 11
Explanation:
Prime factorization is the process of expressing a composite number as the product of its prime numbers. To find the prime factorization of 154, begin by dividing it by the smallest prime number and continue with the next primes until all factors are prime.
Step 1: Start with the smallest prime number, 2.
154 is an even number, which means it is divisible by 2.
154 ÷ 2 = 77
So far, we have:
154 = 2 × 77
Step 2: Factor 77
77 is not even, so it is not divisible by 2. The next smallest prime number is 3, but 77 is not divisible by 3 because 7 + 7 = 14, and 14 is not divisible by 3.
The next prime number is 5. A number divisible by 5 ends in 0 or 5, but 77 ends in 7, so it is not divisible by 5.
Next is 7.
77 ÷ 7 = 11
Now, we have:
77 = 7 × 11
Both 7 and 11 are prime numbers.
So, putting all the steps together:
154 = 2 × 7 × 11
This is the complete prime factorization. All the factors—2, 7, and 11—are prime numbers, and multiplying them gives the original number:
2 × 7 = 14
14 × 11 = 154
Among the answer choices given:
- 2 × 5 × 13 = 130
- 2 × 5 × 11 = 110
- 2 × 7 × 11 = 154 ✅
- 2 × 7 × 13 = 182
Therefore, the correct prime factorization of 154 is 2 × 7 × 11.