__maths__>__Divisibility in Whole Numbers__>__Basics of Divisibility Test__### Divisibility of product of numbers

This page analyses developing divisibility test procedure for numbers given as product of multiple numbers. This forms the foundation to developing other divisibility tests for specific numbers.

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Is `3xx7` a number?

- It does not represent a number, unless the multiplication is simplified
- It is a number given as an expression
- It is a number given as an expression

The answer is "it is a number given as an expression".

Is the number `3xx7` divisible by `3`?

- yes, as the number is a multiple of `3`
- yes, as the number is a multiple of `3`
- cannot decide without finding the product and dividing that by `3`

The answer is "yes, as the number is a multiple of `3`". No need to multiply and then check if the product is divisible by `3`. The divisibility is evident from the given expression.

Is the number `6xx7` divisible by `3`?

- yes, as a factor `6` is divisible by `3`
- yes, as a factor `6` is divisible by `3`
- cannot decide without finding the product and dividing that by `3`

The answer is "yes, as a factor `6` is divisible by `3`". No need to multiply and then check if the product is divisible by `3`. The divisibility is evident from the given expression.

If a multiple is given as a product of two or more numbers (eg: "multiplicand `xx` multiplier"), then if one of them is divisible by a divisor, then the product is divisible by the divisor.

eg: Consider the number `6 xx 25`. The multiplicand `6` is divisible by `3`, so the product `6 xx 25` is divisible by `3`.

**Divisibility test of a Product:** A number is given as product of two numbers : multiplicand `xx` multiplier.

if multiplicand or multiplier is divisible, then the product is divisible.

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