Example 1 : Use Euclid’s algorithm to find the HCF of 4052 and 12576.
Example 2: Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.
Example 3: Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.
Example 4: A sweet seller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the number of that can be placed in each stack for this purpose?
Example 5: Consider the numbers 4n, where n is a natural number. Check whether there is any value of n for which 4n ends with the digit zero.
Example 6: Find the LCM and HCF of 6 and 20 by the prime factorisation method.
Example 7: Find the HCF of 96 and 404 by the prime factorisation method. Hence, find their LCM.
Example 8: Find the HCF and LCM of 6, 72 and 120, using the prime factorisation method.
Example 9: Prove that √ 3 is irrational.
Example 10: Show that 5 – √ 3 is irrational.
Example 11: Show that 3√2 is irrational.
