List of top Mathematics Questions on Real Numbers

Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

Find the HCF and LCM of 96 and 404 by the prime factorisation method and verify that \( \text{HCF} \times \text{LCM} = \) product of the two numbers.

The HCF of 960 and 432 is :

Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the least time.

$(3 \times 11 \times 13 + 3)$ is :

There are two sections A and B of Grade X. There are 28 students in Section A and 30 students in Section B. What is the minimum number of books you will acquire for the class library so that they can be distributed equally among students of Section A or Section B ?

The natural number 1 is :

The LCM of 960 and 240 is :

The HCF of 96 and 432 is :

The natural number 2 is :

The HCF of 960 and 432 is :

Find the smallest 5-digit number exactly divisible by 24 and 36.

The product of the H.C.F. and L.C.M. of two numbers 50 and 20 is :

LCM of the numbers 12 and 20 will be :

If the HCF of 210 and 55 is expressed as \(210 \times 5 + 55m\), then find the value of \(m\).

The natural number 2 is :

The dimensions of a window are 156 cm \(\times\) 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Given that \(\sqrt{5}\) is an irrational number, prove that \(3 + 2\sqrt{5}\) is also an irrational number.

For any natural number n, \( 5^n \) ends with the digit :

Prove that \(2 + 3\sqrt{5}\) is an irrational number given that \(\sqrt{5}\) is an irrational number.

A trader has three different types of oils of volume \(870 \text{ l}\), \(812 \text{ l}\) and \(638 \text{ l}\). Find the least number of containers of equal size required to store all the oil without getting mixed.

If the product of two numbers is 2880 and their H.C.F. is 12, then the value of their L.C.M. is:

Prove that $2\sqrt{2}$ is an irrational number.

HCF of the numbers 49 and 91 will be :

LCM and HCF of two numbers are 182 and 13 respectively. If one number is 26, then other number will be :