Question

There are 288 mangoes,624 bananas and 624 apples.these are to be arranged in heaps containing the same no.of fruits .find the greatest no.of fruits possible in each heap .how many heaps are formed

Answer 1

$\huge{\boxed{\mathbb{ANSWER}}}$

Given Things in the Question are :

The number of Mangoes = 288

The number of Bananas  =  624

The number of Apples     =  624

We can find the number of heaps to be formed by finding the H.C.F. of all ( 527, 646 and 748 ).

Now we are going to find H.C.F by prime factorisation  method :-

288 =  2 × 2 × 2 × 2 × 2 × 3 × 3

624  =  2 × 2 × 2 × 2 × 3  × 13

624  =   2 × 2 × 2 × 2 × 3  × 13

Therefore , H.C.F OF ALL =  2 × 2 × 2 × 2 × 3 = 48

So, 48 HEAPS CAN BE FORMED.

Number of Mangoes in each heap = 288/48

                                              $\implies \boxed{\mathsf{6}}$      

Number of Bananas in each heap   =  624/48

                                              $\implies \boxed{\mathsf{13}}$

Number of Apples in each heap  =  624/48

                                              $\implies \boxed{\mathsf{13}}$

Atlast, I will conclude the whole answer :

$\huge{\boxed{\sf{Number\:of\:Heaps\:formed\:=\:48}}}$

$\huge{\boxed{\sf{Number\:of\:Mangoes\:in\:each\:heap\:=\:6}}}$

$\huge{\boxed{\sf{Number\:of\:Bananas\:in\:each\:heap\:=\:13}}}$

$\huge{\boxed{\sf{Number\:of\:Apples\:in\:each\:heap\:=\:13}}}$