## Math Tests - mathematics practice questions

Remainders after division by 2-4

# 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).

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+

**4**).

Remainders after division by 5-7

# 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).

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+

**4**).

Long division (easy)

Odd or even? (divisibility by 2)

# 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

# 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

## 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.