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FACTORS In this article, we will take the concept of factors further and learn about the sum of factors, and sum of even and odd factors. So, let’s get started.  Sum of Factors: Let us take an example to understand how to calculate the sum of factors. Example: Find...

Previously, we studied about factors, total number of factors, even and odd factors. Now, we’ll proceed further with more concepts related to factors. Perfect Square Factors: If a number is perfect square then its prime factors must have even powers. Consider a...

We all have studied about basic division concepts. In this article, we will further extend this concept to understand factors and multiples.  Factors: If an integer x is completely divided by another integer y, then x is said to be a multiple of y; and y is said to be...

Previously, we have learned the basics of divisibility and various divisibility checks and rules. In this article, we will learn some shortcuts and tricks for divisibility that will help you solve questions quickly. Without wasting time, let’s get going with the...

How do we proceed when we are asked to check whether a composite number is divisible by a given number or not? It can be done using a simple method. Method: Step 1: factorize the number. Step 2: The number will be divisible by the composite divisor when the number is...

How do we proceed when we are asked to check whether a prime number is divisible by a given number or not? It can be done using the concept of seed numbers. Let’s see what this is. Method: Every odd prime number gives unit digit of 1 and 9 in two of their first 10...

So many times we are asked whether a given number is divisible by some number or not. How do we check that? For smaller numbers it is easier for us to answer, but what if we are asked whether 539274921294 is divisible by a random number, say 3, or 5, or 17? How do we...

Every year we have seen questions in CAT and other MBA entrance exams involving direct or indirect application of cubes or cube roots. It has vast applications. Therefore let’s get started with this concept. Cube of a Number: For a given number x, we define, cube of x...

In the previous article, we discussed squares, its importance and properties related to squares. But what are square roots? Let us learn about square roots. Definition: The square root of a number x is that number which when multiplied by itself gives x as the...

SQUARES & SQUARE ROOTS Before starting with this concept, you should know how important this concept is. In Quant and DILR section of CAT or any other MBA entrance exam, there are questions which involve intense calculations. That is where squares and square roots...

In the previous articles, we learnt about an irrational number. But what is a Surd? In this article we will get to know more about Surds and its applications. Definition: An irrational number with root (square root, cube root, etc.) is called a surd. For example: ,...

Important Laws of Exponents and Related Properties In the first article for this lesson, we essentially covered the basic concepts for exponents. In this article, we cover the essential laws that govern this topic. Remember, it is vital for you to learn and memorize...