Q.1 How many pairs of integers (x, y) exist such that the product of x, y and HCF (x, y) = 1080?

Q.2 Find the smallest number that leaves a remainder of 4 on division by 5, 5 on division by 6, 6 on division by 7, 7 on division by 8 and 8 on division by 9?

Q.3 Find the HCF of 2/3, 4/6, 8/27

Q.4 How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?

Q.5 How many pairs of positive integers x, y exist such that HCF (x, y) + LCM (x, y) = 91?

Q.6 Sum of two numbers x, y = 1050. What is the maximum value of the HCF between x and y?

Q.7 The sum of two non co–prime numbers added to their HCF gives us 91. How many such pairs are possible?

Q.8 There are 2 numbers such that a > b, HCF (a, b) = h and LCM (a, b) = l. What is the LCM of a – b and b?

Q.9 6 different sweet varieties of count 32, 216, 136, 88, 184, 120 were ordered for a particular occasion. They need to be packed in such a way that each box has the same variety of sweet and the number of sweets in each box is also the same. What is the minimum number of boxes required to pack?

Q.10 In a large school auditorium, the students are made to sit to watch the programmes. If the teachers make a row of students of 16 each, there will be 12 students left. If they make rows of 24 each, then there will be 20 students left, if they make rows of 25 each, there will be 21 students left and if they make rows of 30 each, there will be 26 students left. What is the minimum number of students present in the school?