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Factors and Multiples

Factors and Multiples. Factors of a Number. Factors of 24. A number may be made by multiplying two or more other numbers together. The numbers that are multiplied together are called factors of the final number. 1 X 24 2 X 12 3 X 8 4 X 6. Multiplication combinations to reach 24.

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Factors and Multiples

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  1. Factors and Multiples

  2. Factors of a Number Factors of 24 A number may be made by multiplying two or more other numbers together. The numbers that are multiplied together are called factors of the final number. 1 X 24 2 X 12 3 X 8 4 X 6 Multiplication combinations to reach 24 {1, 2, 3, 4, 6, 8, 12, 24} A list of its factors

  3. Greatest Common Factor (GCF) Greatest common factor or GCF is the greatest whole number that is a factor of two or more given whole numbers. Example next page

  4. What is the greatest common factor of 36 and 48? Factors of 36: {1, 2, 3, 4, 6, 9, 12, 18, 36} 1 2 3 4 6 9 12 18 36 Factors of 48: {1, 2, 3, 4, 6, 8,12, 16, 24, 48}

  5. What is the greatest common factor of 36 and 48? Factors of 36: {1, 2, 3, 4, 6, 9, 12, 18, 36} 1 2 3 4 6 12 Factors of 48: {1, 2, 3, 4, 6, 8,12, 16, 24, 48} 1 2 3 4 6 12 Which is the greatest common factor? Which factors are common to both numbers?

  6. Greatest Common Factor (GCF) That was too much work. What happened if we forgot to include the 12 in one of the factor list? Want to learn a different way that’s easier? Duh!

  7. Cake Method to find GCF Think of any prime number that divides evenly into both 36 and 48 (a factor of both) Divide both numbers by 2. For this example, I’ll use 2. 18 24 36 48 2

  8. Cake Method to find GCF Think of any prime number that divides evenly into both 18 and 24 (a factor of both) Divide both numbers by 3. 6 8 For this example, I’ll use 3. 3 18 24 36 48 2

  9. Cake Method to find GCF Continue this process until there is no other number besides 1 that is a factor of both numbers. 3 and 4 have no common factor except 1... so you can stop dividing. 3 4 2 6 8 3 18 24 36 48 2

  10. Cake Method to find GCF The product of the numbers along the side of the cake is the GCF of 36 and 48. 2 x 3 x 2 = 12 3 4 2 6 8 3 18 24 36 48 2

  11. Cake Method to find GCF Observe another example. Find the GCF of 64 and 80. 8 x 2 = 16 4 no common factor except 1 5 8 32 40 64 80 2

  12. More Practice • Use the cake method to find the GCF of 14 and 35. • Use the cake method to find the GCF of 42 and 72. • Use the cake method to find the GCF of 12 and 25.

  13. More, More Practice!!  • Jane and her friends are going on a hiking trip on the Appalachian Trail. She wants to take snack bags. She has 36 bananas and 24 bags of peanuts. What is the greatest number of snack bags she can make if each bag has the exact same number of bananas and bags of peanuts? She doesn’t want any bananas or bags of peanuts left over. Explain your answer.

  14. More, More, More Practice  Suppose that Jane’s dog ate 6 bananas. Now what is the greatest number of snack bags she can make with no leftovers?

  15. Still More Practice • Ashley has 27 violet marbles, 54 blue marbles, and 72 white marbles. She wants to divide the marbles into groups so that each group has the same number of each color marble. What is greatest number of groups that Ashley can make? Explain.

  16. Multiples of a Number The products of a number with the natural numbers 1, 2, 3, 4, 5, ...are called the multiples of the number. 7 x 1 = 7 7 x 2 = 14 7 x 3 = 21 7 x 4 = 28 For example: So, the multiples of 7 are 7, 14, 21, 28, and so on.

  17. Multiples of a Number Further examples: multiples of 2 are 2, 4, 6, 8, … multiples of 3 are 3, 6, 9, 12, … multiples of 4 are 4, 8, 12, 16, …

  18. Least Common Multiple (LCM) The smallest common multiple of two or more numbers is called the leastcommon multiple (LCM).

  19. Cake Method to find LCM With the cake method, you can find both the GCF and LCM at the same time! Let’s use a previous example…

  20. Cake Method to find LCM Find the least common multiple of 36 and 48.

  21. Cake Method to find LCM Find the product of the numbers going up and on top of the cake. Let’s make the cake! = 144 144 is the LCM of 36 and 48 3 4 x x 2 6 8 x 3 18 24 x 36 48 2

  22. Cake Method to find LCM Another example: Find the LCM of 16 and 9. Do 16 and 9 have any common factors besides 1? No, they don’t. So their LCM is their product… ? 16 9 X = 144

  23. Cake Method to find LCM Another example: Find the LCM of 5, 6 and 8. Finding the answer by listing multiples of the largest number (8) would eventually lead you to the answer of 120. Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, … Stop at 120 as it is a multiple of both 5 and 6.

  24. Cake Method to find LCM The cake method can be used to find the LCM of 5, 6 and 8. Watch! 5 3 4 x x = 120 x 2 5 6 8

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