The product of all the prime numbers less tha… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Divisibility/Multiples/Factors

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

Correct answer marked below

10^9

10^8

10^7

Correct

10^6

10^5

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Explanation

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Official Explanation

Official

We should find the approximate value of

2*3*5*7*11*13*17*19

to some power of 10.

Approach #1:

2*5=10

;

3*7\approx 20

(actually more than 20);

11*19\approx 200

(actually more than 200);

13*17\approx 200

(actually more than 200);

2*3*5*7*11*13*17*19\approx 10*20*200*200 = 8*10^6 \approx 10^7

.…

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What this question tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Forgetting that 1 is not prime and that every integer divides 0.