Question

How many 3-digits numbers are formed using 1, 2 and 3(without repetition) and divisible by 6?

Answer 1

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For a number to be divisible by 6 :

• It has to be both divisible by 3 and 2

Numbers formed -

• 312
• 132

Answer :- Two numbers are formed

Answer 2

Given,

Three numbers 1, 2, 3.

To Find,

The number of 3 digit numbers that can be formed using 1, 2, 3 without any repetition and which are also divisible by 6.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

The law of any number be divisible by 6, is as follows -

If any number is divisible by 6 then it needs to be divisible by 2 and also the sum of digits be divisible by 3 (Divisible law of 3).

Using three numbers 1, 2, 3 we can form different 3 digit numbers like-

123

132

213

231

312

321

If we calculate the sum of digits of any number, we get (3+2+1=)6. Which is divisible by 3.

Among those 6 numbers, only two numbers 132 and 312 are divisible by 2.

Hence, a total of 2(132 and 312) three-digit numbers can be formed using 1, 2, 3 without any repetition and which are also divisible by 6.