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DIVISIBILITY, FACTORS & MULTIPLES

DUFF’S MATH STUFF… MAKING SENSE OF NUMBER SENSE LESSON 4. DIVISIBILITY, FACTORS & MULTIPLES. WHAT IS DIVISIBILITY???. DIVISIBILITY MEANS THAT A GIVEN NUMBER CAN BE DIVIDED WITHOUT A REMAINDER.

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DIVISIBILITY, FACTORS & MULTIPLES

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  1. DUFF’S MATH STUFF… MAKING SENSE OF NUMBER SENSE LESSON 4 DIVISIBILITY, FACTORS & MULTIPLES

  2. WHAT IS DIVISIBILITY??? DIVISIBILITY MEANS THAT A GIVEN NUMBER CAN BE DIVIDED WITHOUT A REMAINDER. ANY TIME THIS HAPPENS, THE NUMBERS WE DIVIDED BY ARE CALLED FACTORS. MULTIPLYING A GIVEN NUMBER BY ANY OTHER NUMBERS CREATES A LIST OF MULTIPLES. SINCE DIVISION AND MULTIPLYING ARE INVERSE OPERATIONS, FACTORS AND MULTIPLES ARE KIND OF LIKE OPPOSITES

  3. DIVISIBILITY RULES

  4. FACTORS VS MULTIPLES FACTORS MULTIPLES • NUMBERS THAT DIVIDE INTO A GIVEN NUMBER LEAVING NO REMAINDER • THE FIRST FACTOR OF ANY NUMBER IS 1 • THE LAST FACTOR OF ANY NUMBER IS THE NUMBER ITSELF • NUMBERS THAT MULTIPLY TOGETHER TO MAKE THE GIVEN NUMBER ARE CALLED FACTOR PAIRS • NUMBERS CREATED BY MULTIPLYING A GIVEN NUMBER BY CONSECUTIVE COUNTING NUMBERS • THE FIRST FACTOR OF ANY NUMBERS IS THE NUMBER ITSELF • THERE IS NO ‘LAST’ MULTIPLE, A GIVEN NUMBER HAS INFINITE MULTIPLES FACTORS MULTIPLES (COME BEFORE THE NUMBER) (COME AFTER THE NUMBER) 1, 2, 3, 4, 6, 8, 12, 242424, 48, 72, 96, 120 …

  5. FINDING THE LCM WHEN WE COMPARE TWO OR MORE NUMBERS, THE LEAST COMMON MULTIPLE IS THE FIRST MULTIPLE THAT APPEARS ON EACH LIST 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 41, 45 … 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60 … 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, … IN THIS EXAMPLE: LCM OF 3 AND 4 IS 12 LCM OF 3 AND 9 IS 9 LCM OF 3, 4, AND 9 IS 36 HINT: MAKE THE LIST OF MULTIPLES FOR THE LARGEST NUMBER AND SEE IF THE OTHER NUMBERS DIVIDE INTO IT EVENLY

  6. FINDING THE GCF WHEN WE COMPARE TWO OR MORE NUMBERS, THE GREATEST COMMON FACTOR IS THE LARGEST FACTOR THAT APPEARS ON EACH LIST EACH FACTOR SHOULD HAVE A ‘PARTNER’ THAT MULTIPLIES WITH IT TO FORM THE GIVEN NUMBER…THESE ARE CALLED FACTOR PAIRS. DRAWING LINES TO CONNECT FACTOR PAIRS FORMS A FACTOR RAINBOW…THIS IS HOW WE KNOW IF WE HAVE ALL THE FACTORS OF THE GIVEN NUMBER . 24: 1, 2, 3, 4, 6, 8, 12, 24 42: 1, 2, 3, 6, 7, 14, 21, 42 THE ONLY TIME A FACTOR WILL NOT HAVE A PARTNER IS WHEN THE GIVEN NUMBER IS A PERFECT SQUARE (LIKE 5 x 5 = 25)

  7. PRIME AND COMPOSITE NUMBERS A NUMBER WHOSE ONLY FACTORS ARE ONE AND ITSELF IS CALLED A PRIME NUMBER. ALL OTHER NUMBERS, WITH MORE THAN TWO FACTORS, ARE COMPOSITE. 12 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26 27 28 29 30 0 AND 1 ARE NEITHER PRIME NOR COMPOSITE 2 IS THE ONLY EVEN PRIME NUMBER ALL ODD NUMBERS ARE NOT PRIME!

  8. PRIME FACTORIZATION BREAKING A NUMBER DOWN TO A PRODUCT OF ITS PRIME FACTORS IS CALLED PRIME FACTORIZATION. WE CREATE A ‘FACTOR TREE’ TO MODEL THE WAY A NUMBER IS BROKEN DOWN TO PRIMES, EACH LEVEL OF ‘BRANCHES’ SHOWS A FACTOR PAIR, ANY FACTORS THAT ARE NOT PRIME MUST BE BROKEN DOWN TO SMALLER FACTOR PAIRS UNTIL THE END OF EVERY BRANCH IS A PRIME NUMBER. 10 AND 7 ARE A FACTORS THAT HAVE A PRODUCT OF 70… 10 IS NOT PRIME, SO WE BREAK IT DOWN TO A FACTOR PAIR OF 5AND 2 THE ENDS OF THE BRANCHES ARE PRIME: 5, 2, AND 7 SO YOU ARE FINISHED!!! WRITE THE PRODUCT IN DESCENDING ORDER (BIG NUMBERS TO SMALL NUMBERS)

  9. USING PRIME FACTORIZATION TO FIND THE GCF THERE IS ONE 5 AND ONE 2 IN COMMON TO THE PRIME FACTORIZATION OF 40 AND 50, 5 x 2 = 10, SO THE GCF IS 10

  10. LESSON 4 VOCABULARY REVIEW

  11. LESSON 4 VOCABULARY REVIEW

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