Question

what is the smallest four digit number divisible by 6 and 1

Answer 1

Step-by-step explanation:

Rule 1: A number is divisible by 6 if it is divisible by 2 and 3.

Rule 2: A number is divisible by 3 if the sum of its digits is divisible by 3.

Rule 3: A number is divisible by 2 if the number is even.

So starting off with the smallest 4 digit number:

1000

It is divisible by 2

Sum of digits = 1 , which is not divisible by 3

1001

It is not divisible by 2

1002

It is divisible by 2 (from rule 3)

Sum of digits = 3, which is divisible by 3 (from rule 2)

Following rule 1, we have 1002 to be the smallest four digit number divisible by 6.

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Answer 2

Answer:

smallest four digit number is 1000.For a number to be divisible by 6,it must be divisible by 2 and 3.

For a number to be divisible by 2 it must be an even number.For a number to be divisible by 3 sum of digits of number must be divisible by 3.

1000 is even number.But 1+0+0+0=1 which is not divisible by 3.Hence 1000 is not divisible by 3 and so 6.

The next even number is 1002.1+0+0+2=3 which is divisible by 3.

Since 1002 is divisible by both 2 and 3,it is divisible by 6.Thus the smallest 4 digit number divisible by 6 is 1002.