While preparing for quants, here are few things you should know about the properties of the integer:

- Factors and multiples; GCD and LCM
- Odd and even
- Quotient and remainder
- Consecutive numbers and other consecutive sets (odds, evens, multiple of 5, etc.)
- Special properties of 0 [e.g. (any number) + 0 = that number, (any number)*0 = 0]
- Prime numbers
- Special properties of 1 [e.g. 1*(any number) = (that number)]

Let’s start with the definition

An integer is a number with no fractional part or a real number with expressed in a form of p/q with remainder as zero.

For example: 2,45,108, 0, -124, -9 etc.

**GCD and LCM**

Consider 2 numbers 30 and 48

The multiples of the numbers are

30 = 2 x 3 x 5

48= 2 x 2 x 2 x 2 x 3

Common factors are 2 x 3. Therefore HCF or GCD will be 6

LCM will be GCD x rest of the factors = 6 x 5 x 2 x 2 x 2 = 240

**Odd and even**

Following are the properties that should be kept in mind

1) (even) + (even) = (even)

2) (odd) + (odd) = (even)

3) (even) + (odd) = (odd)

4) (even)*(even) = (even)

5) (odd)*(odd) = (odd)

6) (even)*(odd) = (even)

**Quotient and remainder**

When a number p is divided by a number q, where q is not equal to zero and it leaves a remainder r, it can be written as

P = nq + r where n is called a quotient.

**Prime number**

A prime number is a natural number which has only 2 factors: 1 and the number itself

For example: 2, 3, 5, 7, 11, 13………..

When a prime number is divided by 6, it will leave the remainder as 1 or 5. So we can represent the prime number as 6p+1 or 6p-1 where p=1, 2, 3, 4……

Remember that not all the numbers formed by 6p+1 and 6p-1 will be a prime number. For example, place the value of p as 6 in 6p-1. You will get 35, which is not a prime number. But if you place p=6 in 6p+1 you will get 37 which is a prime number. Hence if you place any value for p, either 6p+1 or 6p-1 will yield a prime number.

Probably there is nothing new in this post. Most of them you have already studied in class 10-12. But these are the basic fundamentals which you will need while solving integer based problems in GMAT.

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