# How do I prove 6 + 4 12

## Apply divisibility rules

bettermarks »Math book» Numbers »Divisibility and prime numbers» Divisibility rules »Apply divisibility rules

In these explanations you will learn how to apply the divisibility rules.

### Divisibility through special products

For some numbers you can check the divisibility by these based on their factors. If a number is divisible by 3 and 4, it is also divisible by its product. If a number is divisible by 3 and 5, it is also divisible by its product. If a number is divisible by 2 and 9, it is also divisible by its product.

Rule of divisibility for 12: A number is divisible by 12 if it is divisible by 3 and by 4, otherwise not.

Divisibility rule for 15: A number is divisible by 15 if its checksum, i.e. the sum of its digits, is divisible by 3 and its last digit is 0 or 5, otherwise not.

Rule of divisibility for 18: A number is divisible by 18 if it is even and its checksum, i.e. the sum of its digits, is divisible by 9, otherwise not.

648 is divisible by 12.

646 is not divisible by 12.

If the number is odd, it cannot be divisible by 12.

645 is not divisible by 12.

135 is divisible by 15.

235 is not divisible by 15.

288 is divisible by 18.

729 is not divisible by 18.

### Divisibility of products

Sometimes you already know one of the factors for a product (for example, you know the square numbers). If this factor is divisible by a number, the product is also divisible by this number.

Divisibility rule for products: If a number divides one of the factors of a product, it also divides the product.

However, the reverse is not true: if the product is divisible by a number, every factor does not have to be divisible by this number.

### Divisibility of sums and differences

If you cannot apply the rules of divisibility directly to a number, it is helpful to write the number as a sum or difference. Divisibility of a sum: If every summand is divisible by a given number, then the sum is also divisible by this number. Is only one of the summands is divisible by a number and the other is not, so the sum is not divisible by this number either. Divisibility of a difference: If the minuend and the subtrahend of a difference are divisible by a given number, then the difference is also divisible by this number. If either the minuend or the subtrahend of the two is not divisible by a given number, neither is the difference.

Rule of divisibility of a sum: If a number divides every addend of a sum, it also divides the sum.

Divisibility rule of a difference: If a number divides the minuend and the subtrahend of a difference, it also divides the difference.

6391 is divisible by 7.

729 is not divisible by 7.

Divisibility of a difference

98 is not divisible by 4.

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