# CBSE Class 10-Mathematics: Chapter – 1 Real Numbers Part 7 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 17**:

Find HCF and LCM of and by the prime factorization method.

**Answer**:

**Question 18**:

The HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161, find the other.

**Answer**:

**Question 19**:

Prove that the square of any positive integer of the form is of the same form.

**Answer**:

**Question 20**:

Use Euclid՚s Division Algorithm to find the HCF of and .

**Answer**:

**Question 21**:

Find the largest number which divides 245 and 1029 leaving remainder 5 in each case.

**Answer**:

The required number is the of and i.e.. , and .

**Question 22**:

A shopkeeper has of petrol, of diesel and of kerosene. He wants to sell oil by filling the three kinds of oils in tins of equal capacity. What should be the greatest capacity of such a tin?

**Answer**:

The required greatest capacity is the of and

Now HCF of

capacity is litres