ALGEBRA READINESS

LESSON 4-1

Warm Up

Lesson 4-1 Warm Up

ALGEBRA READINESS

LESSON 4-1

Warm Up

Lesson 4-1 Warm Up

ALGEBRA READINESS

“Prime Factorization” (4-1)

What is a “factor”?

How do you find the factors of a number?

factors: the numbers you multiply together to get a product.Example: the product 24 has several factors.•24 = 1 x 24•24 = 2 x 12•24 = 3 x 8•24 = 4 x 6

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

To find the factors of a number:•Start with 1 times the number.•Try 2, 3, 4, etc.•If you get doubles (such as 4 x 4), then you’re done. Repeats or doubles let you know you’re done.Example: What are the factors of 16?

3 isn’t a factor Z (doesn’t go into 16), so cross it out

Doubles or repeats mean your done!

The factors of 16 are 1, 2, 4, 8, and 16.

1 x 16

2 x 8

3 x ?

4 x 4

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There can be 5 row of 7 seeds in each row or 7 rows of 5 seeds in each row.

1 • 35 Write each pair of factors. Start with 1.

Skip 2, 3, and 4, because 35 is not5 • 7 divisible by 2, 3, or 4. 5 is a factor. Skip

6, because 35 is not divisible by 6.

7 • 5 Stop when you repeat factors.

You have 35 vegetable seeds to plant in your garden.

The seeds must be planted in rows of equal length. How many

seeds can be in each row?

Look for pairs of factors of 35 to find the possible numbers of seeds in each row.

Prime FactorizationLESSON 4-1

Additional Examples

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“Prime Factorization” (4-1)

What are “prime numbers”?

What are “composite numbers:?

What is “prime factorization”?

prime number: numbers that only have two factors: one, and the numberitselfExamples: 3, 5, 7, 11, 31

composite numbers: numbers that have more than two factors

Examples: 6, 15, 18, 30, 100

prime factorization: when a composite number is expressed as the product of prime numbers only

Example: 18 can be expressed as 3 x 3 x 2

Example: 40 can be expressed as 2 x 2 x 2 x 5

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61 has only two factors, 1 and 61. So 61 is prime.

a. 61

b. 65

Since 65 is divisible by 5, it has more than two factors. So 65 iscomposite.

Is each number prime or composite? Explain.

Prime FactorizationLESSON 4-1

Additional Examples

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2 x 50

“Prime Factorization” (4-1)

How do you find the prime factorization of a number?

To find the prime factorization of a number, make a factor tree as follows:.1. Write the product of a prime and composite number under the original

number and draw lines connecting the factors with the original number

2. Circle the prime number, and repeat step 1 with the composite factor.

3. Continue this process until the only numbers you have left are prime numbers.

4. Multiply all of the circled numbers together.

Example: What is the prime factorization of 100?

100

2 x 25

5 x 5

2 is a prime numbers, so we are done with it.

5 is a prime numbers, so we are done with it.

So, the prime factorization of 100 is 2 x 2 x 5 x 5.

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“Prime Factorization” (4-1)

How can we express prime factorization with exponents? “

Since exponents show repeated multiplication (i.e. 34 means “3 x 3 x 3 x 3”), write any repeated prime numbers once and use an exponent to tell how many times that multiplication is repeated.Example: In the previous example, we found the prime factorization of 100 as being 2 x 2 x 5 x 5.•2 x 2 can be expressed in exponent form as 22

•5 x 5 can be expressed in exponent form as 52

So, 2 x 2 x 5 x 5 is more simply put as 22 x 52

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prime 3 30

prime 3 10

prime 2 5

Find the prime factorization of 90.

The prime factorization of 90 is 2 • 3 • 3 • 5 or 2 • 32 • 5.

90

Stop when all factors are prime.

Use a factor tree. Because the sum of the digits of 90 is 9,90 is divisible by 3. Begin the factor tree with 3 • 30.

Prime FactorizationLESSON 4-1

Additional Examples

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Write the prime factorization for each number.

1. 36 2. 150

3. 99 4. 225

22 • 32 2 • 3 • 52

32 • 11 32 • 52

Prime FactorizationLESSON 4-1

Lesson Quiz