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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**Given**: Total number of paintings = 49.

Total number of medals = 35.

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 1**: Prime factorise 49 and 35.

49 = 7 × 7 = 7^{2}

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

Class 10 Maths

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CBSE Class 10 Maths - 2021

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