5th Class Mathematics Factors and Multiples Common Factors

    Common Factors

The same factors of two or more than two different numbers are called common factors.  

Factors of 24 = 1, 2, 3,4, 6, 8, 12, 24

Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.

Here 1, 2, 3, and 6 are the common factors of 24 and 30.  

Co-prime or Relatively Prime Numbers

If two numbers have only one common factor, the numbers are called co-prime or relatively prime numbers.  

Factors of 2 = 1, 2

Factors of 5 = 1, 5

Thus 2 and 5 have only one common factor 1, therefore, 2 and 5 are co- prime numbers.

Factors of 15= 1, 3, 5, 15                                                       

Factors of 8 = 1, 2, 4, 8

15 and 8 have only one common factor which is 1. Therefore, 15 and 8 are the co- prime numbers.

Highest Common Factor (H.C.F) or Greatest Common Factor (G.C.F)

The common factor which is highest among the common factors of two or more than two numbers is called highest common factor of that numbers.      

Find the highest common factors of 12 and 32

Explanation

Factors of 12 = 1, 2 , 3, 4, 6, 12

Factors of 32 = 1, 2, 4, 8, 16, 32

Common factors of 12 and 32 = 1, 2, 4,

The highest common factor of 12 and 32 = 4  

HCF by Division Method

In case of greater numbers it is difficult to find HCF by writing factors. With the help of division method we can get the HCF easily even of greater numbers. Long division method involves the following steps:

Step 1:  The greater number is divided by the smaller number.

Step 2 : The remainder left after subtraction is taken as divisor and divisor as dividend for the next step of division.

Step 3:  The process is repeated unless remainder becomes 0.

Step 4:  The last divisor is the HCF.

Find the HCF of 132 and 64.