HIGHEST COMMON FACTOR(HCF)
But;
what are factors?
A factor of a given number is a number that can divide the given number without a remainder. For instance, 2 can divide 6 without a remainder. Hence, 2 is a factor of 6.
How To Find The Factors Of A Given Number
Starting from 1, find all other numbers that can divide the given number without a remainder.
Example
Find the factors of 48
48 = 1 x 48
= 2 x 24
= 3 x 16
= 4 x 12
= 6 x 12
The numbers in bold text above are all factors of 48 because they can divide 48 without a remainder.
Thus factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Little Tip: when looking for factors of an even number, just divide the even number by 2. The result is the highest factor you can have next to the given number.
E.g Find the factors of 24
Divide 24 by 2 which is 12.
i.e 12 is the highest factor you can have next to 24.
Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24
With our knowledge, let's find the HCF of these numbers using;
Method I
Example:
Find the HCF of 8, 24 & 40
Solution
Factors of 8: 1, 2, 4 and 8
Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24
Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40
The numbers in bold above are all Common in the three given numbers. There's a but here, we are looking for the Highest Common Factor here. So the HCF here out of 1, 2, 4, 8 is 8 obviously.
Thus HCF of 8, 24 and 40 = 8
Method II
Find the HCF of 8, 24 and 40.
Solution
This is probably the simplest and fastest way of finding HCF. Here, we find a number that can divide all 3 numbers without any remainder. When you get to a point where you can not find a number that can divide all 3 numbers, you stop. Period, QED
Check the image below for simplified calculations
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