Question

the g.c.d of two numbers is 7 and the first three quotient are 1,2,3. find those numbers. please say the answer.

Answer 1

7÷7=1 ,14÷7=2 ,21÷7= 3

Answer 2

The two numbers are 49 and 119.

Given:

The g.c.d of two numbers is 7.

The first three quotients are 1,2,3.

To Find:

We have to find those numbers.

Solution:

This is a problem for GCD.

We can easily solve this problem as follows,

Let, those numbers be a and b.

Let, a be the divisor and b be the dividend and the first quotient is 1.

Assume the first remainder be c and the second remainder be d (it's the nonzero remainder) and GCD.

a) b ( 1

 ___

   c ) a ( 2

      ___

       7 = d ) c ( 3

                ___

                  0

Start from below,

c = d×3 + 0 = 7×3 + 0 = 21

a = c×2 + d = 21×2 +7 = 42 + 7 = 49

b = a×2 + c = 49×2 + 21 = 98 + 21 = 119

Hence, the two numbers are 49 and 119.

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