Question

The product of all the prime numbers less than 20 is closest to which of the following powers of 10?

• A. \( 10^9 \)
• B. \( 10^8 \)
• C. \( 10^7 \)
• D. \( 10^6 \)
• E. \( 10^5 \)

Hint:

When approximating large products, round the value to the nearest power of 10 to simplify comparison.

Answer 1

The Correct Option is C

Step 1: Identify the prime numbers less than 20.
The prime numbers less than 20 are: \[ 2, 3, 5, 7, 11, 13, 17, 19 \] Step 2: Calculate the product of these prime numbers.
The product of these primes is: \[ 2 \times 3 \times 5 \times 7 \times 11 \times 13 \times 17 \times 19 = 232792560 \] Step 3: Approximate the product in terms of powers of 10.
We approximate \( 232792560 \) to the nearest power of 10. Since \( 232792560 \approx 2.33 \times 10^8 \), we choose the closest option, which is \( 10^7 \). \[ \boxed{10^7} \]