Dividing and divisibility, factors and multiplies

Division by 2

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Division by 3

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Division by 4

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Division by 5

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Division by 10

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Division by 11

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Remainders after division by 2-4

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Remainder after division

The result of division is not always a nice and round number, e.g. 7÷3. We know that three fits twice into 7. However, 3×2=6. There is 1 still remaining. We call 1 in this case the remainder or left over after dividing (7 is dividend and 3 is divisor).

7÷3

To calculate it you need to find the greatest multiple of the divisor which is still lower than the dividend and subtract it from dividend.

Example:

$$44÷5 $$
$$;→; 5×8=40 ;→; 44−40=4 $$

4 is remainder after division by 5:

$$ 44=5×8+bo4$$


Remainders after division by 5-7

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Remainder after division

The result of division is not always a nice and round number, e.g. 7÷3. We know that three fits twice into 7. However, 3×2=6. There is 1 still remaining. We call 1 in this case the remainder or left over after dividing (7 is dividend and 3 is divisor).

7÷3

To calculate it you need to find the greatest multiple of the divisor which is still lower than the dividend and subtract it from dividend.

Example:

$$44÷5 $$
$$;→; 5×8=40 ;→; 44−40=4 $$

4 is remainder after division by 5:

$$ 44=5×8+bo4$$


Long division (easy)

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Long division by a one-digit number without a remainder

Division of larger numbers is difficult, so we use written forms.

quotientdividendquotientdividenddivisor
$$1752÷8=?$$

The dividend in our example it is 1752 and the divisor is 8. We begin by determining whether the first digit of the dividend (here 1) is greater than or equal to the divisor (here 8). If so, we can divide these numbers. In our case, the first digit of the dividend is smaller than the divisor, so we must also use the second digit in the dividend. So we count how many times 8 fits into 17. We write 2 in the result and calculate the remainder. We multiply the divisor and the result (2×8=16), write the number 16 under 17 and subtract (17−16=1). This remainder must be less than the divisor.

8 175217÷8=2−1621(1)

To the remainder (1) we write another digit (5). Since 15 fits 8 only once, we write 1 in the result. We multiply this result again by the divisor (8) and subtract from 15.

−161521− 878 175215÷8=1(7)

We subtract and write another digit (2) to the remainder 7. We know that 8 fits into 72 exactly nine times, so we write 9 in the result and the remainder is 0. The result of the whole operation is 219. In division, we call the result the quotient.

−1615219− 8728 175272÷8=9

Take a look at another example: 12008÷8

120081×8=8 − 84− 840− 4005×8=401812008815

Sometimes it happens that two zeroes occur in the calculation (in our case the remainder after division was 0 and next digit was 0 as well). In this case we write 0 in the quotient and continue with the next number.

00− 840− 408− 801×8=81200881501

If there occurs dividend smaller than divisor (during calculation in the example below there is 00 and 001), we write 0 in the quotient and continue with the next number.

0− 81001188218÷9=28101899000÷9=01÷9=0


Odd or even? (divisibility by 2)

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Divisibility rules


A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. These numbers are called even numbers. Numbers not divisible by 2 are called odd numbers.

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

A number is divisible by 4 if the number's last two digits are divisible by 4 or the number ends with 00.

A number is divisible by 5 if it ends in 0 or 5.

A number is divisible by 6 if the sum of its digits is divisible by 3 and 2.

A number is divisible by 8 if the number's last three digits are divisible by 8 or the number ends with 000.

A number is divisible by 9 if the sum of its digits is divisible by 9.

A number is divisible by 10 if it ends with 0.



Divisibility by 3

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Divisibility rules


A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. These numbers are called even numbers. Numbers not divisible by 2 are called odd numbers.

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

A number is divisible by 4 if the number's last two digits are divisible by 4 or the number ends with 00.

A number is divisible by 5 if it ends in 0 or 5.

A number is divisible by 6 if the sum of its digits is divisible by 3 and 2.

A number is divisible by 8 if the number's last three digits are divisible by 8 or the number ends with 000.

A number is divisible by 9 if the sum of its digits is divisible by 9.

A number is divisible by 10 if it ends with 0.



Multiples and factors

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Multiples

The multiples of a number are the values in that number’s times table. E.g. the multiples of 5 are 5, 10, 15, 20, 25 and so on.

There is an infinite amount of multiples of any given number.

Factors

Factors of the number are the numbers you multiply together to get this number. A factor is an integer that will divide exactly into another number. E.g. 8 is a factor of 24 because 8 will divide into 24 exactly 3 times with no remainder.

Factor pairs

Factor pairs are two integers which multiply together to make a particular number. For example, the factor pairs of 20 are 1 and 20; 2 and 10; 4 and 5. This means that the factors of 20 are: 1 , 2 , 4 , 5 , 10 and 20. Every integer has a finite number of factors.



   
   

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