📖Definition
Factors and Multiples are closely linked.
Factors
The Factors of a number are all the numbers that divide into it without leaving a remainder.
💡Multiples
The Multiples of a number are its times table. To say one number is 'a multiple of' another number is the same as saying one number is 'divisible by' another number.
Finding Factors
The easiest way to find factors is to write a list of pairs of numbers that can be multiplied together to get the given number.
Start with 1 x the number itself. Then see if 2 will divide into it, then 3, then 4 and so on. If a number doesn't divide, write a dash.
Below is a list of the pairs of numbers that multiply up to make 30.
Diagram
Once you get a number that's already appeared in your list, stop.
The factors are all the numbers in your list above this point which aren't next to a dash.
So, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
💡Testing a Multiple
To see if one number is a multiple of another, divide the larger number by the smaller one. If there's no remainder, then it's a multiple. If there is a remainder then it's not a multiple.
💡Tips/hints
Don't forget 1 and the number itself - they are ALWAYS factors.
Some multiples are easy to spot.
2: any number whose last digit is divisible by 2 is a multiple of 2 (ie. any even number).
4: any number whose last two digits are divisible by 4 is a multiple of 4. So, 716 is divisible by 4 because 16 is divisible by 4
5: any number ending in 0 or 5 is a multiple of 5.
3: any number whose digits add up to a number divisible by 3 is a multiple of 3. So, 52458 is a multiple of 3 because 5+2+4+5+8 = 24 which is divisible by 3.
6: if a number's divisible by 2 and 3 it's a multiple of 6.
9: any number whose digits add up to a number divisible by 9 is a multiple of 9. So, 52452 is a multiple of 9 because 5+2+4+5+2 = 18 which is divisible by 9.
✏️Example
Which numbers between 1 and 10 are NOT factors of 90?
✅Solution
Create a factor list.
Diagram
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
So, the answer to the question is 4, 7 and 8.
✏️Example
One of these numbers is a multiple of 3, which one: 2002, 2004, 2006, 2008?
✅Solution
We can test for multiples of 3 by adding the digits in each number and seeing if their sum is divisible by 3.
Here, 2+0+0+2 = 4, 2+0+0+4 = 6, 2+0+0+6 = 8, 2+0+0+8 = 10. So, as 6 is divisible by 3, 2004 must be a multiple of 3.