Factors and Multiples
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Factors of a given number are all the smaller numbers which can be divided evenly into the given number.
For example: the factors of 48 are 2, 3, 4, 6, 8, 12, 16, and 24. That means that 48 can be divided by all of those numbers.
They are useful when cancelling with fractions.
Highest (Greatest) Common Factor
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The highest (greatest) common factor of two or more numbers is the largest number that can be divided into all of the numbers equally.
Here is how to find out the HCF of 32, 36, and 48.
32 = 2x2x2x2x2
36 = 2x2x3x3
48 = 2x2x2x2x3
Pick out any common numbers.
2 comes up in all three lines twice. Thus, the HCF is 2x2 = 4.
This means that 4 is the largest number that can be divided into the three given numbers.
Multiples
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Multiples of a given number are larger numbers into which the given number can divide evenly. The multiplication tables list them for all numbers up to 12. For higher numbers, they can be easily obtained.
For example: some multiples of 7 are 14, 21, 28, 35, 42, 49, 56, 63, and 70.
They are useful when adding and subtracting fractions having different denominators.
Lowest (Least) Common Multiple
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The lowest (least) common multiple of two or more numbers is the lowest number into which the number can divide evenly.
Here is how to find the LCM of 6, 8, and 9.
6 = 2x3
8 = 2x2x2
9 = 3x3
Pick out the common numbers
2 appears twice, and 3 appears twice. That leaves 2, 2, and 3 without duplication. Count multiples once and singles once. Thus, the LCM is 2x2x2x3x3 = 72.
This means that 72 is the smallest number into which the three given numbers can be divided.
