# THERE ARE 150 STUDENTS WAITING FOR A BOAT TO CROSS A RIVER. THE STUDENTS HAVE TO BE DIVIDED INTO EQUAL GROUPS TO GET INTO DIFFERENT BOATS. IN HOW MANY WAYS CAN YOU GROUP THE STUDENTS SUCH THAT EACH GROUP HAS MORE THAN 5 STUDENTS AND LESS THAN 50 STUDENTS? EXPLAIN ​

For required solution first we find prime factors of 150  , As :

150 = 2 $×$$×$ 5  $×$ 5

And

Multiples of 150 :   1 , 2 , 3 , 5 ,  6 , 10 , 15 , 25 , 30 , 50 , 75 , 150

Here we can see that numbers that lies between 5 and 50 are  :  6 , 10 ,  15 , 25  and 30

Therefore,

We can arrange students in group of 6 , 10 ,  15 , 25  and 30 .                                         ( Ans )