H.C.F of Decimal Numbers.

H.C.F of Decimal Numbers:

Convert the given numbers into same number of decimal places in all the given numbers; then find their H.C.F as if they were integers, and mark in the result as many decimal places as there are in each of the numbers.

Find the H.C.F of Decimal Numbers:

1) 16.5, 0.45 and 15.
Answer:
The given numbers are equivalent to 16.50, 0.45 and 15.00
Step I:   First we find the H.C.F of 1650, 45 and 1500.

 

Step II:  The required H.C.F = 0.15.

                 (or)

(i) Convert the decimal numbers into fractions.

16.5 = 165/10 ; 0.45 = 45/100 ; 15 = 15/1

(ii) H.C.F ( x/a , y/b, z/c ) = H.C.F (x,y,z) / L.C.M ( a,b,c ).

Therefore, H.C.F ( 165/10, 45/100, 15/1 )

= H.C.F (165, 45, 15) / L.C.M ( 10, 100, 1 ).

(iii) H.C.F (165, 45, 15) = 15

       L.C.M ( 10, 100, 1 ) = 100.

(iv) H.C.F ( 165/10, 45/100, 15/1 )

    =  15/ 100 = 0.15 .

 

2) 1.7, 0.51, and 0.153.

Answer:
Step (i): Converting given decimal numbers into like decimals:1700, 510, 153.

 

Step(ii) We find the HCF of 1700, 510 and 153.

Factors of 1700 = 1, 17, 100, 1700.

Factors of 510 = 1, 3, 17, 30, 170, 510.

Factors of 153 = 1, 9, 17, 153.

H.C.F( 1700, 510, 153 ) = 17.

 

Step (iii): The required H.C.F = 0.017.

                   (or)

(i) Converting given Decimal numbers into fractions.

   1.7 = 17/10 ; 0.51= 51/100; 0.153= 153/1000.

 (ii) H.C.F ( x/a , y/b, z/c ) = H.C.F (x,y,z) / L.C.M ( a,b,c ).

Therefore, H.C.F ( 17/10, 51/100, 153/1000 )

= H.C.F (17, 51, 153) / L.C.M ( 10, 100, 1000 ).

(iii) H.C.F (17, 51, 153) = 17

       L.C.M ( 10, 100, 1000 ) = 1000.

(iv) H.C.F ( 17/10, 51/100, 153/1000 )

      H.C.F = 17 /1000 = 0.017.