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How to Find HCF Quickly? And LCM by Using Division Method, Prime Factorization

How to Find HCF

Highest Common Factor and Least common multiple is one of the interesting concepts in Math’s.  So those aspirants who are preparing for competitive or board exam and facing problem in understanding the concept How to Find HCF Quickly Or solving the question, for them we have provided Division Method and Prime Factorization method. We have also furnished some examples to make the concept clearer, calculate HCF and LCM of a Number.

In the below section of this page www.recruitmentinboxx.com you are going to see and understand the concept of the How to Find HCF Easily, How to Find Two Numbers When HCF and LCM Are Given and others.

How to Find HCF

Highest Common Factor can be calculated in two different ways that is Division Method and Prime Factorization method. For the easiness of aspirants we have provided both the methods and techniques how to solve them.

  1. How to Find HCF by Prime Factorization

Prime factorization of the given number is to express a given number as a product of prime factor. It is also known as is also known as complete factorization. There are two ways of finding HCF by Prime Factorization:

  • Tree factorization method
  • One is by dividing

Example: Find prime factorization of 36

Prime factorization of 36 = 2 × 2 × 3 × 3

= 2² × 3²

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  1. How to Find HCF by Division Method

HCF by division method can be calculated in two different ways that are stated below:

Case 1: How to Find HCF of 2 Numbers

Step 1: first of all you have to divide the larger number by the smaller number.

Step 2: Divisor of step 1 is divided by its remainder.

Step 3: Divisor of step 2 is divided by its remainder.

Step 4: Continue this process till we get zero as remainder.

Step 5: Divisor of the last step is the Highest Common Factor.

Case 2: How to Find HCF of 3 Numbers

Step 1: Find out Highest Common Factor of any two numbers.

Step 2: Find out the Highest Common Factor of the third number and the HCF obtained in step 1.

Step 3: Highest Common Factor obtained in step 2 will be the HCF of the three numbers.

  1. How to Find HCF of 3 Numbers Using Euclid’s Division Lemma

Let three no’s are A, B and C

Then find the HCF of A and B

Let their HCF is D

Then find the HCF of C and D

The HCF of c and d is the HCF of A, B and C

Example: Let the numbers be 15, 36, 72

First take the HCF of 15 and 36

36=15×2+6

15=6×2+3

6=3×2+0

So HCF (36, 15) =3

Now HCF (3, 72)

a=72, B=3

72=3×24+0

So HCF (3, 72) =3

Therefore HCF (36, 72, 15) =3

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  1. How to Find HCF of Fractions

We have furnished formulae of HCF and L.C.M which will help you can solve HCF and LCM questions with fraction. Must have a glance!!

  • C.F. = H.C.F. of Numerators/ L.C.M. of Denominators
  • C.M. = L.C.M. of Numerators/ H.C.F. of Denominators

Also Know About:

Permutation and Combination Formula, Aptitude Questions, Problems and Solutions

How to Find LCM:

There are two methods of solving Least common multiple (LCM) that are division Method and Prime Factorization method. We have furnished both the method along with example for the student’s convenience and to make them understand the method.

  1. How to Find LCM by Using Division Method

Step 1: Write the specific numbers in a horizontal line, separate them by using commas.

Step 2: Divide the numbers by using an appropriate prime number that exactly divides at least two of the given numbers.

Step 3: now put the quotient directly under the numbers in the next line. In case the number is not divided exactly, we need to bring it down in the next row.

Step 4: again continue the process we used in step 2 and step 3 until all co-prime numbers are left in the last row.

Step 5: at last you have to multiply all the prime numbers by which you have divided and the co-prime numbers left in the last row. This product is the least common multiple of the given numbers.

Example: Find least common multiple (L.C.M) of 20 and 30 by division method.

Solution:

Least common multiple (L.C.M) of 20 and 30 = 2 × 2 × 5 × 3 = 60

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  1. How to Find LCM by Using Prime Factorization method

Step I:  first of all you have to resolve each given number into its prime factors and express the factors obtained in exponent form.

Step II:  then you have to find the product of the highest powers of all the factors that occur in any of the given numbers.

Step III:  at last, the product obtained in Step II is the required least common multiple (L.C.M).

Example: Find the least common multiple (L.C.M) of 9 and 15 by using prime factorization method.

Step I:

Step II: The product of all the factors with highest powers. = 3^2 × 5 = 3 × 3 × 5 = 45

Step III: Least common multiple (L.C.M) of 9 and 15 = 45

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