Explain why 13233343563715 is a composite number?

a and b are two positive integers such that the least prime factor of a is 3 and the least prime factor of b is 5. Then calculate the least prime factor of (a + b).

What is the HCF of the smallest composite number and the smallest prime number?

Calculate the HCF of 3³ x 5 and 3² x 5².

If HCF (a, b) = 12 and a x b = 1,800, then find LCM (a, b).

What is the condition for the decimal expansion of a rational number to terminate? Explain with the help of an example.

Find the smallest positive rational number by which 1/7 should be multiplied so that its decimal expansion terminates after 2 places of decimal.

What type of decimal expansion does a rational number has? How can you distinguish it from decimal expansion of irrational numbers?

Calculate \(\frac { 3 }{ 8 } \) in the decimal form.

The decimal representation of  \(\\ \frac { 6 }{ 1250 } \)  will terminate 1250 after how many places of decimal?

A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q. when this number is expressed in the form \(\frac{p}{q}\)? Give reason.

Find the HCF of 52 and 117 and also find the values of x and y, if it express in the form 52x + 117y.

Find the HCF of 1,656 and 4,025 by Euclid's division algorithm.

The length, breadth and height of a room are 8m 50 cm, 6 m 25 cm and 4 m 75 cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly.

Find the least number that is divisible by all numbers between 1 and 10 (both inclusive).

An army contingent of 104 members is to march behind an army band of 96 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Explain, why (3 x 5 x 7) + 7 is a composite number?

Show that \(5-\sqrt { 3 } \) is irrational.

Check whether the rational number \(\frac{1}{13}\), is terminating recurring or non-terminating recurring decimal expansion.

Show that the cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.

Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = Product of the two numbers.
26 and 91 

State Fundamental theorem fo Arithmetic. Find LCM of numbers 2520 and 10530 by prime factorization method.

Can the number 6ⁿ, n being number, end with the digit 5 ? Give reasons.