Question

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

a) 10^3

b)10^4

c) 10^5

d) 10^6

Answer 1

To find the product of all prime numbers less than 20, we multiply 2, 3, 5, 7, 11, 13, 17, and 19 together to get 9,699,690, which is closest to the power of 10^6. Correct option is d) 10^6

Step-by-step explanation:

The question is asking for the product of all prime numbers less than 20 to determine which power of 10 it is closest to. To find the product without a calculator, you must know the prime numbers less than 20: 2, 3, 5, 7, 11, 13, 17, and 19. Multiplying these together, you get:

2 × 3 × 5 × 7 × 11 × 13 × 17 × 19 = 9,699,690.

Now let's approximate this product to the nearest power of 10. This number is closer to 10,000,000 (10^7) than to 1,000,000 (10^6) but since the options do not include 10^7, we should look for the next best approximation which is 10^6.

Therefore, the product of all prime numbers less than 20 is closest to 10^6 (option d).