Write the HCF and LCM of the smallest odd composite number and the smallest odd prime number. If an odd number p divides q², then will it divide q³ also? Explain.

2

(a)

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.

2

(a)

If n is an odd integer, then show that n² - 1 is divisible by 8.

2

(a)

Find the LCM of x and y, if xy = 180 and HCF of (x, y) = 5

2

(a)

Find (HCF x LCM) for the numbers 100 and 190.

2

(a)

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

2

(a)

Find HCF of the numbers given below: k, u, 3k, 4k and 5k, where k is any positive integer.

2

(a)

Given that HCF (306, 1,314) = 18. Find LCM (306, 1,314).

2

(a)

Complete the following factor tree and find the composite number x.

2

(a)

Complete the following factor tree and find the composite number x :

2

(a)

Explain whether \(3\times 12\times 101+4\)  is a prime number or a composite number

2

(a)

Can two numbers have 15 as their HCF and 175 as their LCM ? Give reasons.

2

(a)

Check whether (15)ⁿ can end with digit 0 for any \(\\ \\ n\varepsilon N\)

2

(a)

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.

2

(a)

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?

2

(a)