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# What is the largest five-digit integer whose digits have a product equal to the product (7) (6)(5)(4)(3)(2)(1)?

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What is the largest five-digit integer whose digits have a product equal to the product (7)(6)(5)(4)(3)(2)(1)?

Dec 10, 2018

#1
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Just re-arrange your 7 numbers slightly by multiplying 2 x 4 = 8 and put them in order from the biggest to the smallest and you get this: 87,653.

Dec 10, 2018
#2
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98752 still works but is greater than 87653

Guest Dec 10, 2018
#3
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We want the biggest numbers, and we can get a 9 from $$6\times 3$$ which is $$9\times 2$$ .

Therefore, now we have the biggest digit as 9 with 2, 2, 4, 5, and 7 left over.

The next largest digit is probably 8 as $$2\times 4=8$$ , leaving us with 2, 5, and 7.

So far we have 98___ and we can see that $$2\times 5=10, 2\times 7=14, 5\times7=35$$and the tens digits are all less than 7 so now we go decreasing order and get

98752.

You are very welcome!

:P

Dec 11, 2018