PRODUCT OF PRIME NUMBER

Question

The product of all prime number less than 20 is closest to which of the following power of 10? 
a)10^9
b) 10^8
c) 10^7
d) 10^6
e) 10^5

is there any quick way to slove it?

Thanks

Aleehsgonji · Answer

2,3,5,7,11,13,17,19
Mutlitply terms to for products nearest to multiples of 10.
10,21,143,17,19

10^3*4*143*17 ~ 10^3 * 150 * 4 *20 ~10^7

So answer is C.

elliot · Answer

Here is another method to work your way to the answer.

After making a list of prime numbers, I would look for ways to make multiplication easier.

For instance, 19 and 11 are both prime numbers under twenty. If I took the time to times them, my answer would be 209. A quicker way to get an estimate is to shift '1' from '11' to '19'. In effect, making '11' become '10' and making '19' become '20'. Multiplying 10 and 20 gives me 200. A fairly close estimate.

Then, with 7 and 13, I could shift '3' from '13' to '7' making two '10.' 7 times 13 is 91. 10 times 10 is 100. Another close estimate.

Following those we could do 2 x 3 x 5 easily enough in our heads, giving us 30 and leaving us with 17 unmultiplied.

Our new formula is 200 x 100 x 30 x 17. Counting ones and tens places we get '6.' Making our starting estimate 10^6, which we know is 1,000,000. Times 1,000,000 by 2 then 3 then 1.7, which gives us an estimate of 10,200,000. 10^7 is therefore our answer. Either 1.5 or 2 could be used in the place of 1.7 for quicker multiplication.

Had we multiplied numbers individually our answer would have been 9699690. Just under 10^7. This method isn't precise but, when choosing between widely spread answer choices, it normally works.

PRODUCT OF PRIME NUMBER

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