What is HCF?

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HCF and LCM > Important Formulas(HCF) Highest Common Factor(HCF) Highest Common Factor(HCF) of two or more numbers is the greatest number which divides each of them exactly. Greatest Common Measure(GCM) and Greatest Common Divisor(GCD) are the other terms used to refer HCF.

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Highest Common Factor(HCF)
Highest Common Factor(HCF) of two or more numbers is the greatest number which divides each of them exactly.
Greatest Common Measure(GCM) and Greatest Common Divisor(GCD) are the other terms used to refer HCF.
Example : HCF of 60 and 75 = 15 because 15 is the highest number which divides both 60 and 75 exactly.
We can find out HCF using prime factorization method or by dividing the numbers or division method.

Example 1: Find out HCF of 60 and 75
Step 1 : Express each number as a product of prime factors.
60 = 22 × 3 × 5
75 = 3 × 52

Example 2: Find out HCF of 36, 24 and 12
Step 1: Express each number as a product of prime factors.
36 = 22 × 32
24 = 23 × 3
12 = 22 × 3

How to find out HCF - by dividing the numbers (shortcut method)
Step 1: Write the given numbers in a horizontal line separated by commas.
Step 2: Divide the given numbers by the smallest prime number (write in the left side) which can exactly divide all the given numbers.
Step 3: Write the quotients in a line below the first.
Step 4: Repeat the process until we reach a stage where no common prime factor exists for all the numbers.
Step 5: We can see that the factors mentioned in the left side clearly divides all the numbers exactly and they are common prime factors. Their product is the HCF


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