# Important Questions for Chapter 1 - Real Numbers

If you are preparing for the final board exam or any competitive exam, all you need to do is practice. For your benefit, our math subject experts have meticulously prepared a list of important questions for CBSE class 10 Math chapter-wise and topic-wise.

**Important questions based on NCERT syllabus for Chapter 1 - Real Numbers:**

*Question 1*: Use Euclid's division algorithm to find the HCF of: 135 and 225

*Solution*:

Apply Euclid's division lemma to given numbers c and d to find whole numbers q and r such that

c = dq + r, 0 ≤ r < d

Here, c = 225, d = 135

225 = 135 × 1 + 90

Remainder is not equal to 0. Therefore, we apply the same process again on 135 and 90

135 = 90 × 1 + 45

Remainder is not equal to 0 again. Therefore, we apply same process again on 90 and 45.

90 = 45 × 2 + 0

Remainder is equal to 0.

Therefore, HCF of 135 and 225 is equal to 45 which is equal to value of d in the last step.

*Question 2*: Find the L.C.M and H.C.F. of 1296 and 2520 by applying the fundamental theorem of arithmetic method i.e. using the prime factorisation method.

*Solution*:

1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 = 2^4 × 3^4

2520 = 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2^3 × 3^2 × 5 × 7

*Question 3*: Find the LCM and HCF of 510 and 92 and verify that LCM.HCF = product of the two numbers.

*Solution*:

For 510 and 92

510 = 2 × 3 × 5 × 17

92 = 2 × 2 × 23 = 22 × 23

HCF = Product of the smallest power of each common prime factor in the numbers = 2

LCM = Product of the greatest power of each prime factor involved in the numbers

= 22 × 3 × 5 × 17 × 23 = 23460

LCM × HCF = 2 × 23460 = 46920

Product of two given numbers

= 510 × 92 = 46920

Therefore, it is proved that LCM × HCF = product of two given numbers.