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mdfrahim
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Divisible by 4 04 Jul 2009, 15:27
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How many 4 digit numbers are divisible by 4 if no digits are repeated. Sorry I don't know the answer !!!!!
Actually i was trying to understand the explanation given in the following link. The link explained abt. 6 digit numbers, i just thought to make it simple.
https://mathforum.org/library/drmath/view/56154.html



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nightwing79
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Divisible by 4 05 Jul 2009, 02:17
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mdfrahim
How many 4 digit numbers are divisible by 4 if no digits are repeated. Sorry I don't know the answer !!!!!
Actually i was trying to understand the explanation given in the following link. The link explained abt. 6 digit numbers, i just thought to make it simple.
https://mathforum.org/library/drmath/view/56154.html
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Well I have not seen the link but my logic would be thus:

a number is divisible by 4 if the last 2 digits are divisible by 4.

which could be 04,08,12,16,20,24......96. There are 24 numbers. However since numbers cannot repeat -
44,88 are out. So it leaves us with 22 numbers.

for a four digit number to occur the first digit can be 1-9 (9 options) and second number can be 0-9 (10 options)
However again since numbers cannot repeat.

Second number of the 4 digit number = 10 - 2 (2 digits have already been used in by the last 2 digits of the 4 digit number)
= 8

First number of the 4 digit number = 9 - 3 (same logic)
= 6

so each number (04-96) stipulated above can have (6)(8) options.

So total is (6)(8)(22) = 1056 .

is that right?



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