document.write( "Question 387915: What two positive integers multiplied together gives me 1440, and added together gives me 13?
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Algebra.Com's Answer #274229 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "Use this theorem to learn if there can be no solution:\r\n" );
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document.write( "Given positive number N, if positive numbers a and b exist such that\r\n" );
document.write( "ab = N then the minimum value of a+b is \r\n" );
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document.write( "We calculate  which is the smallest\r\n" );
document.write( "value any sum the two positive numbers can have which have product 1440.\r\n" );
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document.write( "But 13 is less than that, so there is no possible solution.\r\n" );
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document.write( "Then it occurred to me that maybe you meant \"subtracted\" instead of\r\n" );
document.write( "\"added together\", for there is a solution to this question:\r\n" );
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document.write( "What two positive integers multiplied together gives me 1440, and subtracted\r\n" );
document.write( "(larger - smaller) gives me 13?\r\n" );
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document.write( "To find out the minimum value of the minimum difference:\r\n" );
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document.write( " 1. First find the square root of 1440. We get 37.94733192\r\n" );
document.write( " 2. Think of the closest factor of 1440 less than that, which is 36\r\n" );
document.write( " 3. Divide 1440 by 36, getting 40\r\n" );
document.write( " 4. Subtract them, getting 4.\r\n" );
document.write( " 5. That's the minimum possible difference.\r\n" );
document.write( " 6. Since 13 is greater than 4, there may be a solution.\r\n" );
document.write( " 7. Get the next smaller factor of 1440 than 36, which is 32.\r\n" );
document.write( " 8. Divide 1440 by 32, getting 45\r\n" );
document.write( "10. Subtract them, getting 13.\r\n" );
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document.write( "That's it.  45×32 = 1440, and 45-32 = 13\r\n" );
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document.write( "So if you meant \"subtracted (larger minus smaller)\" instead of \"added\",\r\n" );
document.write( "this is the answer.  But if you meant \"added\" there is no solution.\r\n" );
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document.write( "Edwin

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