# Simplification Techniques and Tricks

Maths Tricks 0 CommentsSimplification Techniques and Tricks

Classification:-

Natural Numbers (प्राकृत संख्या):

all counting numbers ( 1,2,3,4,5….∞)

Whole Numbers (पूर्ण संख्या):

natural number + zero( 0,1,2,3,4,5…∞)

Integers:

All whole numbers including Negative number + Positive number(∞……-4,-3,-2,-1,0,1,2,3,4,5….∞)

Even & Odd Numbers:

All whole number divisible by 2 is Even (0,2,4,6,8,10,12…..∞) and which does not divide by 2 are Odd (1,3,5,7,9,11,13,15,17,19….∞)

Prime Numbers:

It can be positive or negative except 1, if the number is not divisible by any number except the number itself.(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61….∞)

Composite Numbers:

Natural numbers which are not prime

Co-Prime:

Two natural number a and b are said to be co-prime if their HCF is 1.

**Divisibility**

**Divisible by 2** End with 0,2,4,6,8 are divisible by 2 254,326,3546,4718 all are divisible by 2

**Divisible by 3** Sum of its digits is divisible by 3 375,4251,78123 all are divisible by 3. [549=5+4+9][5+4+9=18]18 is divisible by 3 hence 549 is divisible by 3.

**Divisible by 4** Last two digit divisible by 4 5648 here last 2 digits are 48 which is divisible by 4 hence 5648 is also divisible by 4.

** Divisible by 5** Ends with 0 or 5 225 or 330 here last digit digit is 0 or 5 that mean both the numbers are divisible by 5.

** Divisible by 6** Divides by Both 2 & 3 4536 here last digit is 6 so it divisible by 2 & sum of its digit (like 4+5+3+6=18) is 18 which is divisible by 3.Hence 4536 is divisible by 6.

**Divisible by 8** Last 3 digit divide by 8 746848 here last 3 digit 848 is divisible by 8 hence 746848 is also divisible by 8.

**Divisible by 10** End with 0 220,450,1450,8450 all numbers has a last digit zero it means all are divisible by 10.

**Divisible by 11** [Sum of its digit in

odd places-Sum of its digits

in even places]= 0 or multiple of 11

**Consider the number 39798847**

(Sum of its digits at odd places)-(Sum of its digits at even places)(7+8+9+9)-(4+8+7+3)

(23-12)

23-12=11, which is divisible by 11. So 39798847 is divisible by 11.

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