The product of the first 10 prime numbers is closest to whic

Question

The product of the first 10 prime numbers is closest to which of the following?

A. 6.5 x 10^7
B. 6.5 x 10^8
C. 6.5 x 10^9
D. 6.5 x 10^10
E. 6.5 x 10^11

Bunuel · Accepted Answer

The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. So, we need to find approximate value of 2*3*5*7*11*13*17*19*23*29. # of different approximations are possible. For example: 2*5=10 3*17=~50 (actually more than 50); 7*13=~100 (actually less than 100); 11*19=~200 (actually more than 200) 23*29=667 2*3*5*7*11*13*17*19=~10*50*100*200*667=10^7*667=6.67*10^9. Answer: C. Similar questions to practice: the-product-of-all-the-prime-numbers-less-than-20-is-closest-126587.html the-product-of-the-fir-st-eight-positive-even-integers-is-128135.html the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html the-product-of-the-five-smallest-two-digit-prime-numbers-137076.html Hope it helps.

zw504 · Answer

I just used traditional calculation, but not one by one:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

by observation and estimation:
2*5=10
3*7=21~2*10
11*29~3*100
13*23~3*100
17*19~3*100

so the result ~ 5.4*10^9

All in 2 mins.

dineshril · Answer

1st 10 Prime Number- 2,3,5,7,11,13,17,19,23,29
Let Product of 1st 10 Prime Number =P

Therefore  P=2*3*5*7*11*13*17*19*23*29

Now approximating following as
 5*13=65 
 2*3*7\approx{40} 
 11\approx{10} 
 13\approx{10} 
 17\approx{20} 
 19\approx{20} 
 23\approx{20} 
 29\approx{30}

Therefore  P=65*40*10*10*20*20*20*30 
 P=65*8*10^7  
 P=65*10*10^7  (as  8\approx{10} )
 P=65*10^8 
 P=6.5*10*10^8 
 P=6.5*10^9

Therefore Option 'C'

Thanks
Dinesh

Cinematiccuisine · Answer

i was on the right track. 
a) i listed down first 10 prime numbers as
 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
b) I also multiplied 2 and 5 resulting into 10
c) rest of the numbers were rounded to nearest 10 for ease of multiplication
3* 7 = 21as ~ 20
11 taken as ~ 10
13 taken as ~ 10
17 taken as ~ 20
19 taken as ~ 20
23 taken as ~ 20
29 taken as ~ 30

d) the number acts now as
10 * 20 * 10 * 10 * 20 * 20 * 20 * 30
= some number * 10 power 8
e) if you just multiply 1 * 2 * 1 * 1 * 2 * 2 * 2 * 3 ~= 48

answer is expecting outcome as x.x
hence the final answer can be 48 * 10 power 8 OR 4.8 * 10 power 9

hence C
======
just by rushing through the answers, i made the mistake of just selecting B as it was to power 8. i didn't carefully look into answers showing one decimal point.

saynchalk · Answer

I used a method Bunuel used on another similar question

2*5 = 10
3*7 = 21 = 20
11*19 = 209 = 200
13*23 = 299 = 300
17*29 = 493 = 500

therefore the product of first 10 primes = 2*10 * 2*10 * 2*(10^2) * 3*(10^2) * 5*(10^2)

= 60 * (10^8)
= 6 * (10^9)

Option C works

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The product of the first 10 prime numbers is closest to whic

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