Extra Questions For Class 10 Maths Chapter 1 | Q8

Real Numbers | Word Problem in HCF and LCM

This CBSE class 10 Maths Extra Practice Question is from the chapter Real Numbers. This extra question is a word problem testing you understanding of which one to use - LCM or HCF?

Question - 8: Katya has 49 paintings and 35 medals. She wants to display them in groups throughout her house, each with the same combination of paintings and medals, with none left over. What is the greatest number of groups Katya can display?

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Explanatory Answer | Extra Question in Real Numbers

Given: Total number of paintings = 49.
Total number of medals = 35.

Step 1 - Calculate the Maximum Number of Groups

Let the greatest number of groups that Katya can display be 'n'.
Let the number of paintings in each group be 'p' and the number of medals in each group be 'm'.
49 paintings have been divided into 'n' groups each containing 'p' paintings.
i.e., np = 49
35 medals have been divided into 'n' groups each containing 'm' medals.
i.e., nm = 35

So, 'n' is a factor of 49 and 35.
Because n is the greatest number of groups, n is the HCF of 49 and 35.

Step 2 - Find HCF of 49 and 35

Step 1: Prime factorise 49 and 35.
49 = 7 × 7 = 72
35 = 7 × 5

Step 2: List down common primes.
The only common prime between the 49 and 35 is 7.

Step 3: HCF is the product of the lowest power of common primes.
HCF = 7

The greatest number of groups in which Katya can display paintings and medals is 7.


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