HIGHEST COMMON FACTOR (HCF) & LEAST COMMON MULTIPLE (LCM)

Factor

Also called as divisor of a number. A number that divides exactly into another number and indicates a specific multiple, number or quantity.

One (1) is a factor of all existing numbers because one (1) can be multiplied with any number.

Example:

6=1×2×3

Therefore, 1, 2 and 3 are the factors of the number 6.

How to find Factors of a Number

There are two (02) ways:

1. Factoring through Division Method
2. Factoring through Tree Method

Example-1: Find the factors of number 16 using Division Method.

We will divide 16 by the prime number until  is left as quotient or remainder.

Therefore, the factors of the number 16 are 2×2×2×2 .

Example-2: Find the factors of number 16 using tree method.

Step-1: consider 16 as a parent node.

Step-2: Parent node 16 will have two child nodes, which are 8 and 2 because 8×2=16.

Step-3: Now, node 8 will act as parent node. It will have two child nodes, which are 4 and 2 because 4×2=8.

Step-4: Now, node 4 will act as parent node. It will have two child nodes, which are 2 and 2 because 2×2=4.

Step-5: and now, the process of making tree is completed here, because we reached at the end of tree as we have last two child which are prime numbers. Now, the last step is to write all the nodes which have no child. So, we have factors of 16 as 2×2×2×2.

consider the above diagram, node  has two child nodes which are node  and node . Here, the node  has no child but node  has two child nodes. The process continued till end.

Note

Here, we have learnt how to find factors of a number. Next, we will move to find HCF and LCM.

Highest Common Factor (HCF)

Also called Greatest Common Divisor (GCD), or Greatest Common Denominator. The HCF of two or more numbers is the largest number that divides evenly into both numbers.

Steps in finding the HCF:

1. Find all the prime factors of given numbers.
2. Write given numbers as a multiplication of prime factors.
3. Find which factors are repeating in given numbers and then multiply them to get HCF.

Example-1: Find HCF of 24 and 36.

24=2×2×2×3
36=2×2×3×3

The repeating numbers are highlighted by red color. So, the HCF of 24 and 36 is 2×2×3=12

Example-2: Find HCF of 240 and 924.

240=2×2×2×2×3×5

924=2×2×3×7×11

The repeating numbers are highlighted by red color. So, the HCF of 240 and 924 is 2×2×3=12

Least Common Multiple (LCM)

Also called Lowest Common Multiple, Smallest Common Multiple or Least Common Factor. It is the smallest positive number that is a multiple of two or more numbers.

Multiple: Multiple of a number is obtained by multiplying that number with any other Integer. For example, 9 is a multiple of 3, as 3×3=9.

But 7 is not a multiple of 3.

Note

How to Find the Least Common Multiple

Step-1: Write the multiples of each number (multiply that number with 1,2,3,..).

Step-2: Then look for the smallest number that appears in each list.

Example: Find the LCM of 3 and 5.

Find out multiples of each given number.

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, …

The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, …

Now, look for the first common or same value in both multiples. The value is 15.

Hence, 15 is the LCM of 3 and 5.

Another method:

Find by factorizing using prime numbers as follows:

The LCM is 3×5=15.