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2 years ago

Find a three-digit number, which is 5 times greater than the product of its digits

Mathematics

1 answer:

Anon25 [30]2 years ago

6 0

Answer:

175

Step-by-step explanation:

How would one find a three-digit number which is 5 times as large as the product of its digits?

100a + 10b +c = 5abc

This shows that c must be a multiple of 5. Since it is a digit, c=5 ( c=0 does not work ).

Then:

100a + 10b + 5 = 25ab

This again shows that 10b+5 is a multiple of 25.

By testing all the digits, b=2 or b=7.

If b=2, then

100a + 25 = 50a

which has the solution a= -1/2, not a digit.

if b=7

100a +75 = 175a

Now the solution is a=1, so finally the number is 175. Indeed, 175 = 5*1*7*5.

Does that answer your question..?

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