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# What is the answer to this I am thinking of a number The product of its digit is 12 The number is divisible by 4 your number is greater than 2400 What is your number. workings please?

Updated: 12/21/2022

Gyu19315

Lvl 1
13y ago

Best Answer

The fact that it's larger than 2400 tells us it has at least four digits.

The prime factorization of 12 is 2 x 2 x 3. We can also throw as many ones in there as we like... we know there's at least one, since we have to have at least four digits.

If the last two digits of a number are divisible by four, the number itself is divisible by four. That means it could end with either 12 or 32, both of which are divisible by four. (There's one other possibility as well... the number could end with 16, which is also divisible by four.)

It can't be 2132, since that's less than 2400. 2312 is also less than 2400. The smallest number meeting all the criteria is 3212.

However... this really isn't a very good problem, since 12312, 12132, 12312, 11111111111111232, and literally an infinite number of others also meet all the specifications given.

(The smallest number meeting the given criteria having final digits 16 is 11216.)

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Q: What is the answer to this I am thinking of a number The product of its digit is 12 The number is divisible by 4 your number is greater than 2400 What is your number. workings please?
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