The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ...
The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?
Answer/Solution
10^7
Steps/Work
We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.
# of different approximations are possible.
Approach #1:
2*5=10;
3*7=~20 (actually more than 20);
11*19=~200 (actually more than 200);
13*17=~200 (actually more than 200);
2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107
Answer: C.
Approach #2:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107.
Answer: C.
# of different approximations are possible.
Approach #1:
2*5=10;
3*7=~20 (actually more than 20);
11*19=~200 (actually more than 200);
13*17=~200 (actually more than 200);
2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107
Answer: C.
Approach #2:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107.
Answer: C.