A CAT Number theory question that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts - Factors, Factorials, HCF and LCM, base system & remainders of the above mentioned concepts. In CAT Exam, one can generally expect to get 1 question from CAT Number Systems involving Factors.CAT Quantitiative Aptitude questions from Factors involve ideas like Sum of Factors, Odd factors, Even Factors and so on. CAT Number Systems is an important topic with lots of weightage in the CAT Exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.
The sum of the factors of a number is 124. What is the number?
How many factors of 1080 are perfect squares?
How many factors of 2^{5} * 3^{6} * 5^{2} are perfect squares?
How many factors of 2^{4} * 5^{3} * 7^{4} are odd numbers?
How many factors of the number 2^{8} * 3^{6} * 5^{4} * 10^{5} are multiples of 120?
Number N = 2^{6} * 5^{5} * 7^{6} * 10^{7}; how many factors of N are even numbers?
Numbers A, B, C and D have 16, 28, 30 and 27 factors. Which of these could be a perfect cube?
If a three digit number ‘abc’ has 3 factors, how many factors does the 6-digit number ‘abcabc’ have?
How many numbers are there less than 100 that cannot be written as a multiple of a perfect square greater than 1?
Find the smallest number that has exactly 18 factors.
A number N^{2} has 15 factors. How many factors can N have?
If a three digit number ‘abc’ has 2 factors (where a, b, c are digits), how many factors does the 6-digit number ‘abcabc’ have?
What is the smallest number that has exactly 12 factors?
The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.
The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is
For any natural numbers \(m, n\), and \(k\), such that \(k\) divides both \(m+2 n\) and \(3 m+4 n, k\) must be a common divisor of
The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is
Let \(n\) be the least positive integer such that 168 is a factor of \(1134^n\). If \(m\) is the least positive integer such that \(1134^n\) is a factor of \(168^m\), then \(m+n\) equals
If \(c=\frac{16 x}{y}+\frac{49 y}{x}\) for some non-zero real numbers \(x\) and \(y\), then \(c\) cannot take the value
How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?
Let m and n be natural numbers such that n is even and 0.2 < \\frac{m}{20}), \\frac{n}{m}), \\frac{n}{11}) < 0.5. Then m - 2n equals
How many factors of 2^{4} × 3^{5} × 10^{4} are perfect squares which are greater than 1? [TITA]
How many pairs (m,n) of positive integers satisfy the equation the equation m^{2} + 105 = n^{2}? [TITA]
If N and x are positive integers such that N^{N} = 2^{160} and N^{2} + 2^{N} is an integral multiple of 2^{x}, then the largest possible x is (TITA)
The number of integers x such that 0.25 < 2^{x} < 200, and 2^{x} + 2 is perfectly divisible by either 3 or 4, is [TITA]
The Questions that follow, are from actual XAT papers. If you wish to take them separately or plan to solve actual XAT papers at a later point in time, It would be a good idea to stop here.
Two numbers a and b are inversely proportional to each other. If a increases by 100%, then b decreases by:
The Questions that follow, are from actual IPMAT papers. If you wish to take them separately or plan to solve actual IPMAT papers at a later point in time, It would be a good idea to stop here.
In a class, students are assigned roll numbers from 1 to 140. All students with even roll numbers opted for cricket, all those whose roll numbers are divisible by 5 opted for football, and all those whose roll numbers are divisible by 3 opted for basketball. 'The number of students who did not opt for any of the three sports is
You have been asked to select a positive integer N which is less than 1000 , such that it is either a multiple of 4, or a multiple of 6, or an odd multiple of 9. The number of such numbers is
Placing which of the following two digits at the right end of 4530 makes the resultant six digit number divisible by 6,7 and 9?
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