Factors and Multiples
Factors
A factor of a number will divide that number exactly, without any remainder.Example : 2 is a factor of 16 because 2 goes into 16 exactly 8 times, with no remainder.
But note that 16 also has other factors apart from 2. These other factors are
- 4 : which goes into 16 exactly 4 times
- 8 : which goes into 16 exactly 2 times
- as well as 16 itself : 16 divided by 16 equals 1
- and also 1 : 16 divided by 1 equals 16
So the number 16 has a total of 5 factors.
Example : 24 has the following factors
1,2,3,4,6,8,12,24
Example : 3 is a factor of 9 because 3 divides into 9 exactly, without any remainder.
Example : 3 is also a factor of
27, 18, 30, 15,....and many more
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Which of the following are factors of 72 ?
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4 is a factor of which of these numbers ?
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Example : The numbers 36 and 24 have a common factor of 4. But this not the
Highest Common Factor, because 6 is also a common factor. The number 6 itself
is still not
the required HCF - the HCF is actually 12.
First the easier ones
Example The
multiples of 6 are 6, 12 , 18, 24, 30, etc Note that 6 is a multiple of 6 because
it is equal to 6 multiplied by one.
Highest Common Factor
The Highest Common Factor
(HCF) of two numbers is the highest number that is a factor of both numbers
Finding Factors of
Large Numbers
Some rules
And a few "not so obvious" rules
Multiples
Multiples of a
number are obtained just by multiplying that number by a whole number.
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Which of the following are multiples of 7 ?
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Lowest Common Multiple
The Lowest Common Multiple (LCM) of two numbers is a multiple of both numbers and lower than all other numbers that are also multiples of both the numbers.Example The Lowest Common Multiple of 6 and 4 is 12.
12 is lower than other common multiples like 24, 36, 48, and there is no common multiple of 6 and 4 which is lower than 12.