There are$527\mathrm{apples},646\mathrm{pears},\mathrm{and}748\mathrm{oranges}$. These are to be put in heaps of equal quantities. Find the maximum number of fruits in each heap. How many such heaps would be formed

Given us:

Number of apples =$527$

Number of oranges=$748$

Number of pears= $646$

The fruits are to be arranged in heaps containing the same number of fruits.

To find: The greatest number of fruits

Now, the greatest number of fruits = HCF of $(527,748,and646)$

Firstly, HCF $(527\mathrm{and}646)$

By Euclid's division lemma

Step 1: $527\mathrm{and}646$

$646=527x1+119$

Step 2: $527\mathrm{and}119$

$527=119x4+51$

Step 3: $51\mathrm{and}119$

$119=51\times 2+17$

Step 4 = $51\mathrm{and}17$

$51=17\times 3=0$

The remainder at this stage is 0, the divisor will be the HCF

Now, taking $17\mathrm{and}728$

Step 5:$728\mathrm{and}17$

$728=17\times 44+0$

So, this stage has a remainder of 0. Thus, the HCF of the third numbers$728$ and $17\mathrm{is}17$

Therefore the maximum number of fruits in each heap will be $17$.

A total of 17 heaps are formed.