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# Find the highest common factor of 36 and 84.  Hint: To solve this question we will first of all define what is a Highest common factor (HCF). The highest common factor is the highest number which is a multiple of both the numbers, basically we are looking for the highest number which is common in both the numbers.

HCF means the greatest number which can divide both the given numbers. HCF is also known as Greatest Common Divisor (GCD).
The highest common factor (HCF) is found by multiplying all the factors which appear in the multiple of both of the given numbers.
Here, we have two numbers as 36 and 84.
We will first of all try to find out all the multiples of the number 36 and all the multiples of the number 84.
Writing all the multiples of 36 we have,
36 = 3x2x2x3
Similarly, writing all the multiples of 84 we have,
84 = 7x3x2x2
Taking the common terms from the multiples of both the given numbers gives the HCF of both the numbers. Doing so we have,
HCF = 2x3x2 = 12
Hence, the highest common factor of the given numbers 36 and 84 is 12.

Note: The possibility of error in this question is that you can mistakenly multiply all the multiples of both the numbers which is wrong because we only have to take out the common multiples of both the given numbers and then multiply it to each other to get the desired result.

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