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A factor of a given number is a whole number that divides exactly
into the given number.
So, 4 is a factor of 12 as it divides exactly into 12, and 3 is also a
factor of 12.
Note:
If a number can be expressed as a product
of two whole numbers, then the
whole numbers are called factors of that number.
So, the factors of 12 are 1, 2, 3, 4, 6 and 12.
Common Factors
Common factors are factors that are common to two or more numbers.
Example 16
Find the common factors of 10 and 20.
Solution:
So, the common factors of 10 and 20 are 1, 2, 5 and 10.
Example 17
Find the common factors of 22 and 33.
Solution:
So, the common factors of 22 and 33 are 1 and 11.
Highest Common Factor
The highest common factor (HCF) of two (or more) numbers is the
largest common factor.
So, the common factors of 8 and 12 are 1, 2 and 4; and 4 is the largest
common factor.
Setting out:
Often, we set out the solution as follows:
Example 18
Find the highest common factor of 16 and 32.
Solution:
Key Terms
factors, common factors, highest
common factor, HCF
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