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?

online.maxtute.com

**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

Register in 2 easy steps and

Start learning in 5 minutes!

CBSE Class 10 Maths - 2021

- Real Numbers Revision Class
- Polynomials Revision Videos
- Linear Equations Revision Class
- Quadratic Equations Revision Class
- Arithmetic Progressions Revision Video
- Triangles Revision
- Coordinate Geometry Revision
- Trigonometry Revision Class
- Appl of Trigonometry
- Circles Revision Class
- Areas Related to Circles Revision Videos

1. HCF Word Problem | CBSE Class 10 Math Extra Practice Question **Video Solution **▶

2. Highest Common Factor of 2 Numbers | CBSE 10th Math Extra Practice Question **Video Solution** ▶

3. HCF of 3 numbers | CBSE Class 10 Math Extra Practice Question **Video Solution** ▶

4. Common divisor - different remainders - 2 numbers | CBSE 10th Math Extra Practice Question **Video Solution** ▶

Copyrights © 2016 - 21 All Rights Reserved by Maxtute.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

**Phone:** (91) 44 4500 8484

**Mobile:** (91) 93822 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@maxtute.com