SOLUTION: The product of four consecutive natural numbers is 1680 find the numbers

Question 1049291: The product of four consecutive natural numbers is 1680 find the numbers
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
You would expect them all to be near 10 each, not exactly.

, should not be as bad as it looks because the product being four digits, each of the factors or consecutive natural numbers, should be of one or two digit. Consider 10*10*10*10=1000, only " a little smaller than " your product 1680. Ten is probably one of the numbers.

Simplify to obtain .

The factorizations of 1680?

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Listing some pairs of factorizations of 1680:
.
Using synthetic division, start with 8 and work downward to check for roots.

Only one whole number from 2 to 8 seems to work as a rational root, positive values.

5 | 1 6 11 6 -1680 | | 5 55 330 1680 --------------------------------- 1 11 66 336 0

You could continue on to check 1 and the negative values between negative 1 and negative 9 as possible roots, but see what we have if n=5.

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The consecutive whole number factors are 5, 6, 7, 8.
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CHECK:
OKAY.
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.

Take the square root of 1680: = 40.99 (approx.) From this, it is clear that the numbers are around of 6 and 7. Check 5, 6, 7 and 8: 5*6*7*8 = 1680. Answer. The numbers are 5, 6, 7 and 8.

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