PrimePrimePrimePrime

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MiscMiscMathMathMiscMiscMathMath

Math 170 – Chapter 5Math 170 – Chapter 5

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FINAL

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Primes

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22

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10 Point Question10 Point Question

What is the smallest prime What is the smallest prime number?number?

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Is 209 prime?Is 209 prime?20 Point Question20 Point Question

No. 209=11*19No. 209=11*19

Find the prime Find the prime factorization of 2008.factorization of 2008.

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2*2*2*2512*2*2*251

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30 Point Question30 Point Question

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Any number can be written Any number can be written uniquely as the product of primesuniquely as the product of primes

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40 Point Question40 Point Question

What is the fundamental What is the fundamental theorem of arithmetic?theorem of arithmetic?

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2*2*5*72*2*5*7

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Find the prime factorization of Find the prime factorization of 140.140.

50 Point Question50 Point Question

Composite

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Four.Four.

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What is the smallest What is the smallest composite number?composite number?

10 Point Question10 Point Question

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20 Point Question20 Point Question

Is the 36 digit number consisting only Is the 36 digit number consisting only of 4’s divisible by 3?of 4’s divisible by 3?Here is the number:Here is the number:

444,444,444,444,444,444,444,444,444,444,444,444444,444,444,444,444,444,444,444,444,444,444,444

Yes. The sum of the digits will be Yes. The sum of the digits will be 144, and 144 is divisible by 3. 144, and 144 is divisible by 3.

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30 Point Question30 Point Question

How can you tell if a number is divisible by 6?How can you tell if a number is divisible by 6?

It is divisible by both 2 and It is divisible by both 2 and 33

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Suppose that 24|b. What else must Suppose that 24|b. What else must divide b?divide b?

40 Point Question40 Point Question

1, 2, 3, 4, 6, 8, and 1, 2, 3, 4, 6, 8, and 1212

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Show that if a|b and a|c, then a|(b+c).Show that if a|b and a|c, then a|(b+c).50 Point Question50 Point Question

Since a|b, b can be made out of rods of length a. Since a|b, b can be made out of rods of length a. Since a|c, c can also be made out of rods of length a. Since a|c, c can also be made out of rods of length a.

By putting these two together, you get b+c, which By putting these two together, you get b+c, which can also me made of rods of length a. Thus a divides can also me made of rods of length a. Thus a divides

(b+c)(b+c)

aaaa aaaaaa

bbaa aa aa

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GCF

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1, 2, 3, 6, 7, 14, 21, 1, 2, 3, 6, 7, 14, 21, 4242

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List all the factors of 42List all the factors of 42

10 Point Question10 Point Question

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Use prime factorization Use prime factorization to find the GCF of 12 and to find the GCF of 12 and

30.30.

20 Point Question20 Point Question

12 = 2*2*312 = 2*2*330 = 2*3*530 = 2*3*5

Primes in common: 2& 3. GCF Primes in common: 2& 3. GCF = 2*3=6= 2*3=6

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GCF(75,120) = GCF(75,45)= GCF(75,120) = GCF(75,45)= GCF(30,45) = GCF(15,30) = GCF(30,45) = GCF(15,30) =

GCF(15,15) = 15.GCF(15,15) = 15.

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Use the subtraction method to Use the subtraction method to find the GCF of 75 and 120.find the GCF of 75 and 120.

30 Point Question30 Point Question

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6 cookies per tray6 cookies per tray

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Joe the Baker baked up 84 spice cookies and 90 Joe the Baker baked up 84 spice cookies and 90 sugar cookies. Joe is planning on selling the sugar cookies. Joe is planning on selling the cookies in trays. Each tray should contain only cookies in trays. Each tray should contain only one type of cookie, and each tray, regardless of one type of cookie, and each tray, regardless of the type should contain the same number of the type should contain the same number of cookies. Joe wants to use the least number of cookies. Joe wants to use the least number of trays. How many cookies should he put on each trays. How many cookies should he put on each tray?tray?

40 Point Question40 Point Question

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2*2*3*7*112*2*3*7*11

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Find the GCF of these three Find the GCF of these three numbers:numbers:2*2*2*3*3*5*7*112*2*2*3*3*5*7*112*2*3*3*3*7*11*17*192*2*3*3*3*7*11*17*192*2*2*2*3*5*7*11*19*232*2*2*2*3*5*7*11*19*23

50 Point Question50 Point Question

LCM

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7, 14, 21, 28, 35, 427, 14, 21, 28, 35, 42

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10 Point Question10 Point Question

List the first 6 multiples List the first 6 multiples of 7.of 7.

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Carol is laying down rods that are 8 units Carol is laying down rods that are 8 units long. Mike is laying down rods that are 6 long. Mike is laying down rods that are 6 units long. If they both started at the units long. If they both started at the same place, when will the ends of their same place, when will the ends of their rods line up again?rods line up again?

20 Point Question20 Point Question

When they each have reached a When they each have reached a length of 24 units.length of 24 units.

Find the LCM of 48 and 40 using the Find the LCM of 48 and 40 using the prime factorization of each number.prime factorization of each number.

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240240

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30 Point Question30 Point Question

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40 Point Question40 Point Question

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Juan will only by a CD if it has exactly Juan will only by a CD if it has exactly 14 songs on it. Marty will buy a CD only 14 songs on it. Marty will buy a CD only if it has exactly 12 songs on it. If they if it has exactly 12 songs on it. If they have the same number of songs in their have the same number of songs in their collection, what is the fewest number of collection, what is the fewest number of CD’s each owns?CD’s each owns?Juan owns 6, Marty owns 7. They both Juan owns 6, Marty owns 7. They both

have 84 songs in their collection.have 84 songs in their collection.

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50 Point Question50 Point Question

Find the LCM of the following Find the LCM of the following numbers numbers 2*2*2*3*3*5*7*112*2*2*3*3*5*7*112*2*3*3*3*7*11*17*192*2*3*3*3*7*11*17*192*2*2*2*3*5*7*11*19*232*2*2*2*3*5*7*11*19*23

2*2*2*2*3*3*3*5*7*11*17*19*22*2*2*2*3*3*3*5*7*11*17*19*233

Misc. Math

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The Associative Property of The Associative Property of Addition.Addition.

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Which property of addition Which property of addition does the following does the following

demonstrate?demonstrate?(a + b) + c = a +(b + c)(a + b) + c = a +(b + c)

10 Point Question10 Point Question

Explain how to do the Explain how to do the following problem using following problem using

mental math.mental math.21X36 + 21X6421X36 + 21X64Use the distributative property to make it Use the distributative property to make it

21X(36+64) Add the compatible numbers, 21X(36+64) Add the compatible numbers, then multiply to get 2100.then multiply to get 2100.

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20 Point Question20 Point Question

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30 Point Question30 Point Question

Use the range method to Use the range method to get estimates for get estimates for

236+153.236+153.

Low: 300, high 500.Low: 300, high 500.

Explain how to use the Explain how to use the compensation method to find compensation method to find

248+296.248+296.

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40 Point Question40 Point Question

I would take 4 from the 248 and add it to I would take 4 from the 248 and add it to the 296 so the sum becomes 244 + 300 = the 296 so the sum becomes 244 + 300 =

544.544.

I guess you could also take 2 from the 296 I guess you could also take 2 from the 296 and add it to the 248 so the problem and add it to the 248 so the problem

becomes 250 + 294, but my way results in becomes 250 + 294, but my way results in an easier sum.an easier sum.

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Final QuestionFinal Question

They are perfect squares. For example, They are perfect squares. For example, 36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, 36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18,

3636

Most numbers have an even number of Most numbers have an even number of factors. For example, there are 6 numbers factors. For example, there are 6 numbers

that evenly divide into 12 (1, 2, 3, 4, 6, & 12), that evenly divide into 12 (1, 2, 3, 4, 6, & 12), 4 numbers that divide evenly into 15 (1, 3, 5, 4 numbers that divide evenly into 15 (1, 3, 5, & 15) and only 2 numbers that divide into 19. & 15) and only 2 numbers that divide into 19.

What is special about numbers with an odd What is special about numbers with an odd

number of factors? number of factors?