H.C.F of Three Numbers Using Long Division Method

H.C.F for Three numbers by using Long Division Method:

Step-1: First, we need to find H.C.F of any two numbers.

Step-2: Now, we need to find out the H.C.F of the third number and the H.C.F obtained in step-1.

Step-3: H.C.F obtained in step-2  will be the H.C.F of the three numbers.

 In a similar way by following the steps in finding the H.C.F for Three numbers, we can find out H.C.F for more than three numbers by using Long Division method.

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

1) 255, 136, 170.

Answer:

(i) H.C.F  of  two numbers 136, 170 = 34.

(ii) Now, we need to find out H.C.F of third number:255, and the H.C.F obtained in Step-1 : 34.

i.e; Need to find H.C.F for 34 and 255.

(iii) H.C.F obtained in step-2 is the H.C.F of the three numbers.

Therefore, H.C.F of 255, 136, 170 = 17.

 

2) 144, 252, 630.

Answer:

(i) H.C.F of 144 and 252 = 36.

(ii) Now, we need to find out H.C.F of third number:630, and the H.C.F obtained in Step-1 :36 .

i.e; Need to find H.C.F for 36 and 630.

 

(iii) H.C.F obtained in step-2 is the H.C.F of the three numbers.

Therefore, H.C.F of 144, 252, 630 = 18.

 

3) 639, 1065, 1491.

Answer:

(i) H.C.F  of 1065 and 1491 = 213.

 

(ii) Now, we need to find out H.C.F of third number:639, and the H.C.F obtained in Step-1: 213 .

i.e; Need to find H.C.F for 213 and 639.

(iii) H.C.F obtained in step-2 is the H.C.F of the three numbers.

Therefore, H.C.F of 639, 1065, 1491 = 213.

 

4) 144, 180, 192.

Answer:

(i) H.C.F  of 180, 192 =  12.

(ii) Now, we need to find out H.C.F of third number: 144, and the H.C.F obtained in Step-1: 12.

i.e; Need to find H.C.F for 12 and 144.

(iii) H.C.F obtained in step-2 is the H.C.F of the three numbers.

Therefore, H.C.F of 144, 180, 192 = 12.

H.C.F of Numbers Using Common Division Method

H.C.F of Numbers Using Common  Division Method:

Step-1: Divide the given numbers together by the smallest prime number which can exactly divides all the given numbers.

Step-2: Repeat the process until we reach a stage where no common prime factor exists for all the numbers.

Step-3: We can see that the factors mentioned in the left side clearly divides all the numbers exactly and they are common prime factors.

Step-4: Multiply those common prime factors to get the H.C.F.

 

Find the H.C.F of numbers by common division method:

1) 24, 36 and 60.

Answer:

The left side Prime factors which divides the given numbers exactly are 2, 2, 3.

Therefore, H.C.F of 24,36 and 60 = 2 * 2 * 3 = 12.

 

2) 136 ,68, 102.

Answer:

The left side Prime factors which divides the given numbers exactly are 2, 17.

Therefore, H.C.F of 136, 68 , 102 = 2 * 17 = 34.

3) 43, 91, 183.

Answer:

All the given numbers are Prime numbers. So, the factors of Prime numbers are 1 and number itself.

Therefore, H.C.F of 43, 91, 183 = 1.

 

4) 48, 56, 72.

Answer:

The left side Prime factors which divides the given numbers exactly are 2, 2, 2

Therefore, H.C.F of 48, 56, 72 = 2 * 2 * 2 = 8.

 

5) 44, 66,110.

Answer:

The left side Prime factors which divides the given numbers exactly are 2, 11.

Therefore, H.C.F of 44, 66, 110 = 2  * 11 = 22.

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.