15 pastries and 12 biscuit packets have been donated for a school fete. These are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each. How many biscuit packets and how many pastries will each box contain?

Given: Number of pastries = 15

Number of biscuits = 12

To find: Number of pastries and biscuits in a box

Concept Used:

Euclid's division lemma:

If there are two positive integers a and b,

then there exist unique integers q and r such that,

a = bq + r where 0 ≤ r ≤ b.

Explanation:

To find the maximum of two things we calculate the HCF.

Here we must find HCF of 15 and 12.

As 15>12.

By Euclid’s lemma,

15 = 12× 1 + 3

As 3 ≠ 0,

Apply Euclid’s lemma in 12 and 3.

12 = 3× 4 + 0

Now remainder is 0.

So HCF of 15 and 12 is 3.

So, number of identical boxes= 3

Hence,

Number of pastries in a box = Number of pastries/number of boxes

= 15/3

= 5

Number of biscuits in a box = Number of biscuits/number of boxes

= 12/3

= 4