Tougher problems on HCF and LCM

In the HCF of two numbers which were prime to each other, the quotients are 2,2,7,2 on finding HCF by method of division. Find the two numbers.

 Answer:

Since the numbers are prime, the HCF is 1.

Now following the method of finding HCF by the method of division, we get

Final Dividend = 1x2 = 2

In the pen ultimate division, the divisor is 2, the quotient is 7 and the remainder is 1.

So, the dividend is = 2x7 + 1 = 15

In the prior division, the divisor is 15, the quotient is 2 and the remainder is 2.

So, the dividend is = 15x 2 + 2 = 32

Therefore, the smaller of the two numbers is 32.

The next number is the divisor = 32 x 2 + 15 = 79

So, the two numbers are 32 and 79.

                                                               

Check:

                               32) 79 (2

                                     64

                                       15) 32 (2

                                              30

                                                2)15 (7

                                                   14

  1) 2 (2

2

x