PLAYING WITH

NUMBERS

FACTORS FACTORS ARE NUMBERS YOU CAN MULTIPLY TOGETHER TO MAKE ANOTHER NUMBER.

EXAMPLE: 3X4=12, SO 3 AND 4 ARE FACTORS OF 12. 2X6=12, SO 2 AND 6 ARE ALSO FACTORS OF 12.

MULTIPLESA MULTIPLE IS THE RESULT OF MULTIPLYING A NUMBER BY AN INTEGER (NOT A FRACTION)

EXAMPLE: 12 IS A MULTIPLE OF 3, BECAUSE 3X4=12. 12 IS ALSO A MULTIPLE OF 2, BECAUSE 2X6=12.

HCF HIGHEST COMMON

FACTOR AND LCM

LOWEST COMMON

MULTIPLE

HCF HIGHEST COMMON FACTORTHE HCF IS THE HIGHEST NUMBER THAT DIVIDES EVENLY INTO TWO OR MORE NUMBERS. IT IS THE LARGEST NUMBER POSSIBLE TO SIMPLIFY THOSE NUMBERS.

EXAMPLE: FACTORS OF 12: 1, 2, 3, 4, 6, 12. FACTORS OF 16: 1, 2, 4, 8, 16.

THE COMMON FACTORS ARE: 1, 2, 4 AND THE HIGHEST IS 4, SO 4 IS THE HFC OF 12 AND 16.

LCM LOWEST COMMON MULTIPLETHE LCM IS THE LOWEST COMMON MULTIPLE OF TWO OR MORE NUMBERS.

EXAMPLE: MULTIPLES OF 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40,… MULTIPLES OF 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50,…

THE MULTIPLES THAT APPEAR IN BOTH ROWS ARE: 20, 40, 60, 80,… AND THE SMALLEST IS 20, SO THE LCM OF 4 AND 5 IS 20.

SHORT DIVISION

METHODS OF HCF

HIGHEST COMMON

FACTOR AND LCM

LOWEST COMMON

MULTIPLE

HCF SHORT DIVISION METHOD

THE SHORT DIVISION METHOD ALLOWS YOU TO FIND THE HCF OF TWO NUMBERS QUICKLY. STEPS:1. DIVIDE BOTH NUMBRES BY A COMMON NUMBER

UNTIL NONE CAN BE FOUND2. MULTIPLY THE LEFT COLUMN

HCF SHORT DIVISION METHOD EXAMPLE

1. DRAW A LINE ACROSS AND A LINE DOWN.

2. WRITE THE TWO NUMBERS ON THE LINE GOING ACROSS TO THE RIGHT.

3. DIVIDE THE TWO NUMBERS UNTIL NONE CAN BE FOUND.

4. MULTIPLY THE LEFT COLUMN.

LCM SHORT DIVISION METHODTHE SHORT DIVISION METHOD ALLOWS YOU TO FIND THE LCM OF TWO NUMBERS QUICKLY.

STEPS:1. DIVIDE BOTH NUMBERS BY A COMMON NUMBER UNTIL NONE

CAN BE FOUND. 2. MULTIPLY THE LEFT COLUMN AND THE BOTTOM ROW.

LCM SHORT DIVISION METHOD EXAMPLE

1. DRAW A LINE ACROSS AND A LINE DOWN. 2. WRITE THE TWO NUMBERS ON THE LINE

GOING ACROSS TO THE RIGHT. 3. DIVIDE THE TWO NUMBERS UNTIL NONE

CAN BE FOUND. 4. MULTIPLY THE LEFT COLUMN AND THE

BOTTOM ROW.

RULES OF DIVISIBILITY

OBJECTIVETO USE RULES OF DIVISIBILITY FOR LARGER NUMBERS

• Definition• Divisibility: the ability to determine what numbers a

larger number is divisible by evenly.

• There are some tricks that we can use to help us determine what numbers larger numbers are divisible by without doing long division.

RULES OF DIVISIBILITY FOR 2• A number is divisible by 2 if the one’s digit is

even. • Therefore, any number that ends with 0, 2, 4,

6, or 8 is divisible by 2 evenly.• Examples: 78; 102; 1,046; 6,550

RULES OF DIVISIBILITY FOR 3• A number is divisible by 3 if the sum of the digits is a

multiple of three.• Is 96 divisible by 3?• In order to find out, we must add the digits 9 + 6

9 + 6 = 15• Is 15 a multiple of 3??? YES, which means that 96

is divisible by 3.

RULES OF DIVISIBILITY FOR 3 CONTINUED…• How about 108… is this number divisible by 3???

• Add the digits together1 + 0 + 8 = 9

• Is 9 a multiple of 3??? YES, which means that 108 is divisible by 3!

RULES OF DIVISIBILITY FOR 4• A number is divisible by 4 if the last two digits are divisible by

four.• Let’s take 124 for example:• The last two digits in 124 are 24

• Is 24 divisible by 4? YES, this means that 124 is divisible by 4!

RULES OF DIVISIBILITY FOR 4 CONTINUED…• How about 1,312… is this number divisible by 4???

• The last two digits in 1,312 are 12

• Is 12 divisible by 4??? YES, again, this means that 1,312 is divisible by 4!

RULES OF DIVISIBILITY FOR 5• A number is divisible by 5 if the one’s digit is 0 or 5.

• So, any number that ends with a 0 or a 5 is definitely divisible by 5!

• Examples: 10; 95; 115; 690; 4,615

RULES OF DIVISIBILITY FOR 6

1. A number is divisible by 6 if the sum of the digits is a multiple of three and even.

2. A number is also divisible by 6 if the number is divisible by both 2 and 3.

RULES OF DIVISIBILITY FOR 6 CONTINUED…• 804• 804 is an even number

8 + 0 + 4 = 1212 is a multiple of 3, which means that 804 is

divisible by 6.816816 /3=272 , 816/2=408816 is

divisible by 6.

RULES OF DIVISIBILITY FOR 7• A number is divisible by 7 : 1) Take the last digit 2) Double it 3) Then subtract it from the rest of the number. Is this

number a multiple of 7?

RULES OF DIVISIBILITY FOR 7 CONTINUED…• Example: 203• The last digit of 203 is 3• Double 3, means 3 x 2 = 6• Subtract 6 from 20

20 – 6 = 14• Is 14 a multiple of 7?? YES, which means that 203 is

divisible by 7.

RULES OF DIVISIBILITY FOR 8

• A number is divisible by 8 if the last three digits are divisible by eight.

• Examples:9,640 640 ÷ 8 = 80 so the whole number, 9,640, is

divisible by 8

77, 184 184 ÷ 8 = 23 so  77,184 passes this divisibility test.

It does not matter how big is the number, this trick will work on all numbers.

RULES OF DIVISIBILITY FOR 9• A number is divisible by 9 if the sum of the digits

is divisible by 9. • Example: 702• Add the digits: 7 + 0 + 2 = 9• Is 9 divisible by 9? YES, which means that

702 is also divisible by 9.

RULES OF DIVISIBILITY FOR 9 CONTINUED…• Example: 3,276

• Add the digits: 3 + 2 + 7 + 6 = 18

• Is 18 a multiple of 9??? YES, which means that 3,276 is also divisible by 9.

RULES OF DIVISIBILITY FOR 10• A number is divisible by 10 if the last digit is 0.• Like 7620• Last digit is 0• So its divisible by 10• 7620/10=762

RULES OF DIVISIBILITY FOR 11• A number is divisible by 11 when the sum of the odd numbered digits is

subtracted from the sum of even numbered digits and the result is divisible by 11

• Like 5181913 • 5+8+9+3=25 , 1+1+1=3• 25-3=22• 22/11=2• So, 5181913 is divisible by 11.

IF ANY NUMBER IS DIVISIBLE BY ALL THE FACTORS

OF THE NUMBER YOU WANT TO DIVIDE IT FROM, IT

IS DIVISIBLE BY THAT NUMBER.

MADE BY- ARNAV JAIN