<p>Hi! There's a math question from the collegeboard sat book that I didn't get.. I was wondering if anyone could help me:</p>
<p>How many integers greater than 20 and less than 30 are each the product of exactly two different numbers, both of which are prime?</p>
<p>The answer is supposed to be 3.</p>
<p>Thanks!</p>
<p>21 (3,7)
26 (13,2)
22 (11,2)</p>
<p>Just try out all the numbers: 21=7<em>3 so it works; 22=11</em>2 so it works; 23=23<em>1 so no (1 isn't prime); 24=2</em>2<em>2</em>3 so no; 25=5<em>5, not different so no; 26=13</em>2 so it works; 27=3<em>3</em>3 so no; 28=2<em>2</em>7 so no; 29=29*1 so no.</p>
<p>21, 22 and 26 work-3 numbers.</p>
<p>Oh... but isn't 21 also the product of 1 and 21, etc?</p>
<p>start off with 2. try the other primes. 11, 13 produce numbers in the range.
with 3, only 7 does it (the next prime is 11)
none with 5</p>
<p>Did the question mean exactly two different prime numbers plus other factors?</p>
<p>every number is a product of 1 and itself. you need to just reason it out, i guess</p>
<p>I see, thanks! =)</p>
<p>1 isn't prime. So numbers like 21, where the factors are 1, 3, 7, and 21, only 3 and 7 are prime. Actually, the question is worded poorly...instead of reading "each the product of exactly two different numbers, both of which are prime," it would be better if it said "each the product of exactly two different prime numbers." Though that still isn't the greatest wording, either.</p>