# CBSE Class 10-Mathematics: Chapter – 1 Real Numbers Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## 3 Marks Questions

**Question 1**:

Use Euclid՚s division algorithm to find the HCF of:

(i) and

(ii) and

(iii) and

**Answer**:

(i) and

We have ,

So, we apply the division lemma to and to obtain

Here remainder , we apply the division lemma again to and to obtain

We consider the new divisor and new remainder , and apply the division lemma to obtain

Since that time, the remainder is zero, the process get stops.

The divisor at this stage is

Therefore, the HCF of and is .

(ii) and

We have ,

So, we apply the division lemma to and to obtain

Since we get the remainder is zero, the process stops.

The divisor at this stage is ,

Therefore, HCF of and is .

(iii) and

We have ,

So, we apply the division lemma to and to obtain

Here remainder , we apply the division lemma again to and to obtain

Here remainder , we apply the division lemma again to and to obtain

Since we get the remainder is zero, the process stops.

The divisor at this stage is ,

Therefore, HCF of and is .

**Question 2**:

Find the greatest number of digits exactly divisible by and .

**Answer**:

The greater number of 6 digits is .

LCM of , and is .

**Question 3**:

Prove that the square of any positive integer is of the form or for some integer .

**Answer**:

Let , when and

Numbers are and

**Question 4**:

cartons of coke can and cartons of Pepsi can are to be stacked in a canteen. If each stack is of the same height and is to contain cartons of the same drink. What would be the greater number of cartons each stack would have?

**Answer**:

We find the of and

So, greatest numbers of cartons is .