H.C.F of Two Numbers by Long Division Method.

HIGHEST COMMON FACTOR BY LONG DIVISION:

1) Long Division for two numbers:

Step-1: In the given two numbers, we need to divide the largest number (Dividend) with smallest number(Divisor) at once. The remainder (R₁) obtained in this step is the divisor for the next step.

Step-2: In this step, the Divisor in the step-1 is the dividend in the step-2 and R₁ is the Divisor. The remainder (R₂) obtained in this step is the Divisor for the Step-3.

Step-3:  The Divisor in the step-2, becomes the Dividend in this step. This Process of Division is continued till we get the Remainder ‘0’.

Step-4: This is the last step, in which we get the Remainder as ‘0’.The divisor in the last step is the Highest Common Factor.

For Bigger numbers we find H.C.F by using Long Division method.

Find H.C.F of two numbers by Long Division method:

1) 248 and 492.

Answer:

(i) We need to Divide largest number,Dividend= 492 with smallest number, Divisor= 248  at once.The Remainder in this step is  244,  which is the new Divisor for the second step.

(ii) Now, the Dividend is 248  and the Divisor is  244. In this step, after dividing the numbers at once we get the remainder as  4,  which is a new Divisorfor the next step.

(iii) Here, the Divisor is  4 and Dividend is 244. When we divide 244 with 4 at once we get the Remainder as ‘0’. By this we stop the division further. The Divisor: 4, in this step is the Highest Common Factor.(H.C.F).

   

Therefore,H.C.F of 248 and 492 = 2.

 2) 1584 and 1683.

Answer:

i) Dividend = 1683; Divisor = 1584 ; Remainder = 99.

ii) Divisor = 99 ; Dividend = 1584 ; Remainder = 0.

Here, we stop the division and the H.C.F = 99.

 

Therefore, H.C.F of 1584 and 1683 = 99.

 3) 1044 and 1512.

Answer:

(i) Dividend = 1512 ; Divisor = 1044 ; Remainder = 468.

(ii) Dividend = 1044; Divisor = 468 ; Remainder = 108.

(iii) Dividend = 468; Divisor = 108 ; Remainder = 36.

(iv) Dividend = 108 ; Divisor = 36 ; Remainder = 0. This is the last step.

Therefore, Highest Common Factor of 1044 and 1512 = 36.  

 

4) 396 and 420.

Answer:

(i) Dividend = 420; Divisor = 396; Remainder = 34.

(ii) Dividend = 396; Divisor = 34; Remainder = 22.

(iii) Dividend = 34; Divisor = 22; Remainder = 12.

(iv) Dividend = 22; Divisor = 12; Remainder = 10.

(v) Dividend = 12; Divisor = 10;  Remainder = 2.

(vi) Dividend = 10; Divisor = 2;  Remainder = 0.This is the end of the division.

Therefore, H.C.F of 396  and  420 = 2.