# Divisor and dividend of a number.Divisibility by sum and difference by a number.

The operations addition and multiplication are always possible, but operations subtraction and division without remainder are possible at certain conditions. In subtraction we can easily see if it is possible or not: it is enough the minuend to be higher or equal to the subtrahend. In division it is not always so simple to see if a number is divisible without remainder. There are certain cases of division in which by some indications of the numbers, we can see in advance if the division can be done without remainder or not.

#### Divisor and dividend

If a number can be divided by another without remainder, we say that the first number is dividend or it is divisible on the second and the second is divisor of the first number.

For example: Number 8 is dividend to 4 and 4 is divisor to 8.But 8 is not dividend to 3 and 3 is not a divisor to 8

15 is dividend to 1, 3, 5, 15 and every one of these numbers is divisor to 15

Every number is dividend to itself. 1 is dividend to all numbers. For example: 4/4 = 1; 7/7 = 1; 9/1 = 1; 12/1 = 12

#### Divisibility by sum with number

Numbers 6 and 14 are divisible by 2; Their sum 20 is also divisible by 2
Numbers 12, 18, 30 are divisible by 6; Their sum 60 is also divisible by 6

If the addends are divisible individually by a number , their sum is divisible by that number too.

We can use this property of the sum to see if a number is divisible by another, without doing the division

For example: Is 742 divisible by 7?
To answer the question, we expand 742 to 2 addends 742 = 700 + 42. Because both 700 and 42 are divisible by 7 and their sum 742 is also divisible

15 is divisible by 3, but 10 is not divisible by 3. Their sum 25 is not divisible by 3

10 and 30 are divisible by 5, but 8 is not divisible by 5 and their sum 48 is also not divisible by 5

If only one addend is not divisible by a number , the sum is also not divisible by that number

#### Divisibility by difference with number

40 and 12 are divisible by 4. Their difference 28 is also divisible by 4

If the minuend and the subtrahend are divisible individually by a number , their difference is divisible by that number too.

We use this property to determine if a number is divisible by another one, without making the division
For example: Is 792 divisible by 8? If we add 8 to 792 we get 800, or 800 - 8 = 792

The minuend(800) and the subtrahend(8) are divisible by 8, that is why the difference 792 is divisible by 8 too

40 is divisible by 10, but 12 is not divisible by 10. Their difference 28 is not divisible by 10

40 is not divisible by 6, but 12 is divisible by 6. Their difference 28 is not divisible by 6

If only the minuend or the subtrahend is not divisible by a number, the difference is also not divisible by that number.

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