Factors and Multiples Factors of a Number A

Factors and Multiples

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

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

What is the greatest common factor of 36 and 48? Factors of 36: {1, 1 22, 3, 3 4, 4 6, 6 9 9, 12 12, 18 18, 36} 36 Factors of 48: {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

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

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?

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

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

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

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

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

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 For example: 7 x 2 = 14 So, the multiples of 7 are 7 x 3 = 21 7 x 4 = 28 7, 14, 21, 28, and so on.

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, …

Common Multiples that are common to two or more numbers are said to be common multiples. For example: Multiples of 2 are 2, 4, 6, 8, 10, 12 12, 14, 16, 18 18, … Multiples of 3 are 3, 6, 9, 12, 15, 18, … So, common multiples of 2 and 3 are 6, 12, 18, …

Example 2: Find the common multiples of 4 and 6. Solution: 12 24 Multiples of 4 are 4, 8, 12, 16, 20, 24, 36 28, 32, 36, … Multiples of 6 are 6, 12, 18, 24, 30, 36, 12 24 36 … So, the common multiples of 4 and 6 are 12, 24, 36, …

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

Least Common Multiple (LCM) To find the least common multiple (LCM) of two or more numbers, list the multiples of the larger number and stop when you find a multiple of the other number. This is the LCM.

Least Common Multiple (LCM) Find the least common multiple of 6 and 9. Solution: List the multiples of 9 and stop when you find a multiple of 6. LCM is 18 Multiples of 9 are 9, 18, … Multiples of 6 are 6, 12, 18, …

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

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

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

Birthday 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 X 9 = 144

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

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