Question

The HCF of two natural numbers is 3. Which of these could be the product of the two numbers?
a)417
b)436
c)711
d)762
pls help me fast​

Answer 1

Answer:

711 is right Answer.

417 is wrong .

Answer 2

Given HCF of two numbers , find the possible product of the numbers

Explanation:

1. let the given two numbers be 'x' and 'y' and their HCF be denoted by 'h' is $h=3$, then we have,                                                                                     [tex]x=h(K)\\ y=h(K')[/tex]           ->here,  K and K' are some positive integer ($\neq 0$)
2. hence, the product 'p' of the given numbers will be,                                          $p=xy=h^2(K'')$    ->here, K'' is some positive integer($\neq 0$)                                      
3. hence the product is of the form , $p=9(K'')$                                                            
4. now if $p=417$                                                                                                             we have, $p=3x139$  ->hence it is not a possible product
5. now if $p=436$                                                                                                                                                we have, $p=2x2x109$  ->hence it is not a possible product
6. now if $p=711$                                                                                                            we have, $p=3x3x79$   ->hence it is a possible product
7. now if $p=762$                                                                                                            we have, $p=2x3x127$   ->hence it is not a possible product
8. the possible product out of the given options is (c)$711$