A number is a factor if it divides another number with no remainder. For example, 4 is a factor of 12, because 12 \div 4 = 3 with no remainder.
Every number will have at least two factors, 1 and the number itself. Thinking again about the number 12, we know that 12 \div 1 = 12 with no remainder, and 12 \div 12 = 1 with no remainder, so 12 and 1 are both factors of 12.
If we're finding all the factors of a number we are trying to find all the numbers we can multiply together to make that specific number.
Let's find the factors of 12 by starting at 1 and trying to find a number that multiplies with it to make 12:
\begin{array}{c} &1 &\times &12 &= &12 \\ &2 &\times &6 &= &12 \\ &3 &\times &4 &= &12 \end{array}
Remember, 4 \times 3 = 3 \times 4, and both of these numbers already appear, so we can move to the next number up. 5 does not divide evenly into 12, and we already know 6 is a factor because 6 \times 2 = 2 \times 6. Once you have checked all numbers up to half of the number (in this case 6 is half of 12) you can stop.
So, the factors of 12 are all the numbers on the left hand side: 1, 2, 3, 4, 6 and 12.
Watch this video for some more examples:
Notice that in the above example, each factor had a corresponding factor it multiplied with to give the 'target' number. These two numbers are known as a factor pair.
We can construct any number by using its factor pairs. Every number will have at least one factor pair, 1 and itself.
When we're completing factor expressions we need to think of a second number we can use to complete an expression. We can do this by counting up or dividing.
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We can use multiplication tables to help us work out factors of a number.
Complete this table of factor pairs:
\text{Factor of pairs of } 75 |
---|
(⬚, 75) |
(⬚, 25) |
(5, ⬚) |
Write down all the factors of 10.
A number is a factor of a particular value if it divides the value with no remainder.
Each factor with a corresponding factor is multiplied to give the 'target' number. These two numbers are known as a factor pair.
A number is a multiple of another if it can be made by multiplication. For example, 15 is a multiple of 5, because 15 = 3 \times 5.
To find multiples of a number we start by multiplying by 1, then by 2, then by 3, and so on. To find multiples of 2 we work our way through starting at
\begin{array}{c} &2 &\times &1 &= &2 \\ &2 &\times &2 &= &4 \\ &2 &\times &3 &= &6 \end{array}
... and can keep going forever. Our work so far tells us that the first three multiples of 2 are 2,\,4, and 6.
Here are some other examples:
Use the apple below to find the first 12 of any number from 1 to 12.
To find the nth multiple of a number, we multiply that number by n.
Write the first five multiples of 8.
To find the nth multiple of a number, we multiply that number by n.