What is the prime factorization of 140?

What is the prime factorization of 140?

• A. 2 x 70
• B. 2 x 3 x 5 x 7
• C. 2 x 2 x 5 x 7
• D. 2 x 2 x 2 x 5 x 7

Answer: (C)

To find the prime factorization of 140, we start by dividing 140 by the smallest prime number, which is 2. Performing this division gives us: 140 ÷ 2 = 70. Next, we factor 70 further. Again, we can divide it by 2: 70 ÷ 2 = 35. At this point, we need to factor 35. The next smallest prime number is 3, but since 35 is not divisible by 3, we move to the next prime number, which is 5: 35 ÷ 5 = 7. Now, we have reached 7, which is a prime number itself. We can now compile all the prime factors we found: 140 = 2 × 2 × 5 × 7. This can also be expressed as \(2^2 × 5 × 7\), which matches the answer provided. Thus, the prime factorization of 140 is correctly identified as 2 × 2 × 5 × 7. This demonstrates how breaking down a composite number into its prime factors leads to the final expression in its simplest form.

To find the prime factorization of 140, we start by dividing 140 by the smallest prime number, which is 2. Performing this division gives us:

140 ÷ 2 = 70.

Next, we factor 70 further. Again, we can divide it by 2:

70 ÷ 2 = 35.

At this point, we need to factor 35. The next smallest prime number is 3, but since 35 is not divisible by 3, we move to the next prime number, which is 5:

35 ÷ 5 = 7.

Now, we have reached 7, which is a prime number itself. We can now compile all the prime factors we found:

140 = 2 × 2 × 5 × 7.

This can also be expressed as (2^2 × 5 × 7), which matches the answer provided. Thus, the prime factorization of 140 is correctly identified as 2 × 2 × 5 × 7. This demonstrates how breaking down a composite number into its prime factors leads to the final expression in its simplest form.