Question

Find the greatest number that will divide 148 246 and 623 leaving remainders 4 6 and 11 respectively

Answer 1

Solution :-

Remainder in case of 148 = 4

Number = 148 - 4 = 144

Remainder in case of 246 = 6

Number = 246 - 6 = 240

Remainder in case of 623 = 11

Number = 623 - 11 = 612

Now, we have find the H.C.F. of 144. 240 and 612

     
        _____________
    2  | 144, 240, 612
        |____________
    2  |   72, 120, 306   
        |____________
    3  |   36,  60,  153  
        |____________
        |   12,  20,  51
        |

H.C.F. of 144, 240 and 612 = 2*2*3 = 12

Therefore, the required number is 12 that will divide 148, 246 and 623 leaving remainders 4, 6 and 11 respectively.

Answer.

Answer 2

Answer:

12

Step-by-step explanation:

'Q' represents quotient and 'r' represents remainder

148 = Q1 +r1   =  Q1 +4

Q1 = 148-4 = 144

246 = Q2 + r2   = Q2 +6

Q2 = 246-6 = 240

623 = Q3 + r3 = Q3 +11

Q3= 623-11 = 612

the greatest number that will divide 148 246 and 623 leaving remainders 4 6 and 11 respectively is the

HCF(Q1,Q2,Q3)

HCF(144, 240,612) = 12

    || 144,240,612

2   || 72, 120, 306

2   || 36, 60, 153

3   || 12, 20, 51

HCF = 2 x 2 x 3 = 12