Use the divisibility rules to determine which of the following numbers 330 is divisible by. (Check all that apply.)

2
3
5
7
11

The numbers that divide 330 are 2, 3, 5 and 11.

In order to find divisibility, there are certain rules for different numbers. If a number is divisible by two numbers then it is also divisible by their product.

The given number is 330.

The divisibility rules for the number given can be applied one by one as follows,

Divisibility for 2,

For a number to be divisible by 2 its unit digit must be 0, 2, 4, 6 or 8.

Thus, 330 is divisible by 2.

Divisibility for 3,

For a number to be divisible by 3 sum of the digits of the number must be divisible by 3.

Since sum of the digits of 330 is 6 which is divisible by 3, 330 is also divisible by 3.

Divisibility for 5,

A number should either end with 0 or 5 in order to be divisible by 5.

Thus, 330 is divisible by 5 as it ends with 0.

Divisibility for 7,

For a number to be divisible by 7, the digit at ones place multiplied by 2 and then subtracted from the remaining digits must be divisible by 7.

Here, in 330 this rule is applied as,

33 - 2 × 0 = 33

Since 33 is not divisible by 7, 330 is also not divisible.

Divisibility for 11,

The difference of the sum of the digits at even place to the odd place must either be zero or divisible by 11.

In 330, 3 + 0 - 3 = 0.

Thus, 330 is divisible by 11.

Hence, the given number 330 is divisible by 2, 3, 5 and 11.

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