Playing with numbers
- 2. 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.
- 3. A 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.
- 5. THE 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.
- 6. THE 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.
- 8. 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 FOUND 2. MULTIPLY THE LEFT COLUMN
- 9. 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.
- 10. THE 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.
- 11. 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.
- 13. • 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.
- 14. • 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
- 15. • 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.
- 16. • How about 108… is this number divisible by 3??? • Add the digits together 1 + 0 + 8 = 9 • Is 9 a multiple of 3??? YES, which means that 108 is divisible by 3!
- 17. • 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!
- 18. • 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!
- 19. • 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
- 20. 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.
- 21. • 804 • 804 is an even number 8 + 0 + 4 = 12 12 is a multiple of 3, which means that 804 is divisible by 6. 816816 /3=272 , 816/2=408816 is divisible by 6.
- 22. • 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?
- 23. • 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.
- 24. • 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.
- 25. • 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.
- 26. • 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.
- 27. • 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
- 28. • 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.