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 The answer is C. Is there a way to find the answer without multiplying all the prime nos? Any help would be much appreciated

We're not concerned with the exact value, so we will make approximations and collect as many 0s as we can. (2*3*5)*(7*11)*13*17*19 = (30*77)*(13*17)*(19) ~ 2200*200*20 ~ 8.8 X 10^6 10^6 < 8.8 X 10^6 < 10^7 (8.8 X 10^6 is closer to 10^7 than 10^6) [spoiler](C)[/spoiler] is the answer

Pugalenthi wrote: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 The answer is C. Is there a way to find the answer without multiplying all the prime nos? Any help would be much appreciated We can regroup the numbers, 2, 3, 5, 7, 11, 13, 17, and 19, to multiply them. 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 = (2 * 5) * (3 * 7) * 11 * 13 * 17 * 19 = 10 * 21 * 11 * 13 * 17 * 19 Now approximating, we get 10 * 20 * 10 * 10 * 20 * 20 = 8 * 10^6, which is 10^7 appr. The correct answer is C.

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