How to Find HCF Quickly? Of Two/Three/Four & Large Numbers Shortcut Tricks

How to Find HCF

There numerous of students in the beginning who face difficulty in finding the HCF quickly and they wonder that How to Find HCF Quickly? Here we have provided Shortcut Tricks to Find HCF, students can also learn techniques of finding the highest common factor of Two/Three/Four & Large Numbers. On the below section of this page we have guided step by step method to Find HCF, so to learn the helpful ways students are required to go through the entire post thoroughly.

Students who are eager to learn that how to find HCF quickly are advised to carefully read the page and as we have guided all the necessary things from the beginning to make you learn it more clearly. You just need to scroll down the page and fetch all essential details about finding highest common factor of a number. Our hardworking team unit of www.privatejobshub.in has well asserted this page for the ease of the aspirants, so mut have a careful glance..

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How to Find HCF

As we have guided here the techniques to find the highest common factor quickly from the beginning, so it is therefore very essential to clear the basics. In this concern we have first defined the basic things which the students must know before learning the shortcuts, must go through it carefully..

Factor

A factor of a given number is every number that divides exactly into that number.

Example:

Write down all factors of 10.

10 = 2 x 5, so numbers 2 and 5 are factors of 10.
 Also 10 = 10 x 1, so 10 and 1 are factors of 10.

The factors of 10 are 1, 2, 5, 10.

Note: Number 1 and the number itself are always factors of any number.

Common Factors

When two (or more) numbers have the same factor, that factor is called a common factor.

Example:

Find all the common factors of 12 and 18.

Factors of 12 are 1, 2, 3, 4, 6, 12.

Factors of 18 are 1, 2, 3, 6, 18.

The common factors of 12 and 18 are 1, 2, 3 and 6.

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Highest Common Factor (H.C.F).

The Highest Common Factor (H.C.F) of two (or more) numbers is the largest number that divides evenly into both numbers. 

• In other words the H.C.F is the largest of all the common factors.
• The common factors or of 12 and 18 are 1, 2, 3 and 6. 
• The largest common factor is 6, so this is the H.C.F. of 12 and 18.
• It is very easy to find a H.C.F. of small numbers, like 6 and 9 (it is 3) or 8 and 4 (it is 4). 
• The best way is to keep finding the factors of the smaller number, starting from the largest factor. The first factor of the smaller number that is also a factor of the larger number is a H.C.F. 
• The H.C.F is useful when simplifying fractions.

Finding the H.C.F. of Big Numbers:

• For larger numbers you can use the following method:
• Find all prime factors of both numbers.
• Write both numbers as a multiplication of prime numbers.
• Find which factors are repeating in both numbers and multiply them to get  H.C.F (why?)

Example:

Find the Highest Common Factor (H.C.F.) of 240 and 924.

Solution:

Finding all prime factors of 240:

• We will start with the smallest prime number and we will divide 240 into it if we can (the divisibility rules come handy). 
• We will do the same with the result (or quotient), and we will keep dividing by prime numbers until we have 1 as a quotient. 
• Each time we write the prime factor to the right and the quotient below:

240|2     2 is a factor of 240;   240 divided by 2 is 120 120|2     2 is a factor of 120;   120 divided by 2 is 60   60|2     2 is a factor of 60;      60 divided by 2 is 3   30|2     2 is a factor of 30;      30 divided by 2 is 15   15|3     3 is a factor of 15;      15 divided by 3 is 5     5|5     5 is a factor of 5;         5 divided by 5 is 1      1

240 = 2 x 2 x 2 x 2 x 3 x 5

NOTE: There are other methods for finding all prime factors of a number, for example a factor tree.

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Finding all prime factors of 924:

924|2     2 is a factor of 924;    924 divided by 2 is 462  462|2     2 is a factor of 462;    462 divided by 2 is 231  231|3     3 is a factor of 231;    213 divided by 3 is 77    77|7     7 is a factor of 77;      77 divided by 7 is 11    11|1     11 is a factor of 11;    11 divided by 11 is 1      1|

924 = 2 x 2 x 3 x 7 x 11

Multiply the factors which repeat in both numbers  to get the H.C.F.

The Highest Common Factor is 2 x 2 x 3 = 12

Highest Common Factor Of Two Numbers By Division Method:

1. Find highest common factor (H.C.F) of 180 and 270 by using division method.

Solution:

Step 1: Here we need to divide 270 by 180.

[Divide the larger number by the smaller one]

Step 2: The first divisor is 180 and the remainder is 90, so we need to divide 180 by 90.

[Divide the first divisor by the first remainder]

Step 3: The remainder becomes 0.

Step 4: Therefore, highest common factor = 90.

[The last divisor is the required highest common factor (H.C.F) of the given numbers].

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Highest Common Factor Of Three Numbers By Division Method:

Step 1:

First of all find the highest common factor (H.C.F) of any two of the given numbers.

Step 2:

• Now find the highest common factor (H.C.F) of the third given number and the highest common factor (H.C.F) obtained in Step 1 from first and the second number. 
• Let us consider some examples to find the highest common factor (H.C.F) of three numbers by division method.
• (To find the highest common factor of three numbers by using division method is discussed here step by step.)

1. Find highest common factor (H.C.F) of 184, 230 and 276 by using division method.

Solution:

Let us find the highest common factor (H.C.F) of 184 and 230.

Highest common factor of 184 and 230 = 46

Now find the H.C.F. of 276 and 46

Highest common factor of 276 and 46 = 46

Therefore, required highest common factor (H.C.F) of 184, 230 and 276 = 46

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