common factors identify common factors of a set of whole numbers 5.3d identify prime &...

Common Factors*Identify Common Factors of a Set of Whole Numbers 5.3D *Identify Prime & Composite Numbers using Patterns in Factor Pairs 5.5B

Reasoning Mind Academy: Common Factors

REMEMBER: A is the answer to a multiplication problem.

Key Words:

prime composite(2) factors

product factor pairs

prime factorization common factor

Greatest Common Factor (GCF)


REMEMBER: A product is the answer to a multiplication problem.

Key Words:

prime composite factors





Definition: are numbers that are multiplied together to get a product.

Key Words:



(prime factorization) common factor



Definition: Factors are numbers that are multiplied together to get a product.

Key Words: prime composite factors

product factor pairs(prime factorization) common factor



REMEMBER: Factor x Factor = Multiple or Product

Example: (Factor) 7 x (Factor) 11 = (Product) 77


Definition: A number is a whole number that has only two factors: one and the number itself.

Key Words:






Definition: A prime number is a whole number that has only two factors: one and the number itself.

Key Words:






Definition: A number is a whole number that has three or more factors.

Key Words:






Definition: A composite number is a whole number that has three or more factors.

Key Words:






REMEMBER: numbers can be odd OR even.

Key Words:

prime composite(2) factor





REMEMBER: Composite numbers can be odd OR even.

Key Words:

prime composite factor





REMEMBER: is special! It is neither prime nor composite!

Which Number????


REMEMBER: One is special! It is neither prime nor composite!


REMEMBER: are two numbers that, when multiplied, will always result in the same product, no matter the order of the numbers. Example: 2 x 4 = 8 or 4 x 2 = 8

Key Words: prime composite(2) factor

product factor pairsprime factorization common factor



REMEMBER: Factor pairs are two numbers that, when multiplied, will always result in the same product, no matter the order of the numbers. Example: 2 x 4 = 8 or 4 x 2 = 8

Key Words: prime composite factor




Definition: A composite number written as the product of numbers is called the

______ of the number.

Example: 2 x 2 x 3 = 12Key Words:

prime composite(2) factor





Definition: A composite number written as the product of prime numbers is called the prime factorization of the number.

Example: 2 x 2 x 3 = 12Key Words: prime composite(2) factor




REMEMBER: means to “factor”, “fracture”, or “break down” numbers.

Key Words: prime composite(2) factor

product factor pairsprime (factorization) common factor



REMEMBER: Factorization means to “factor”, “fracture”, or “break down” numbers.

Key Words:



prime (factorization) common factor



Definition: A is a number that is a factor of two or more given numbers.

Example: 3 is a factor of both 33 and 24





Definition: A common factor is a number that is a factor of two or more given numbers.

Example: 3 is a factor of both 33 and 24





Definition: The (hint: GCF ) of two or more

numbers is the greatest whole number that is a factor of each of the numbers.

Key Words:



prime factorization common factors

Greatest Common Factor


Definition: The Greatest Common Factor (hint: GCF ) of two or more numbers is the greatest whole number that is a factor of each the numbers.

Key Words:



prime factorization common factors

Greatest Common Factor


Example 1) Find all the factors of the number shown and classify them as prime or composite numbers.

a. 15

Step 1: Find ALL factor pairs that, when multiplied, will give a product of 15. Check numbers 1-10 as possible factors using (÷) if necessary. 15

1 15

3 5


Example 1) Find all the factors of the number shown and classify them as prime or composite numbers.

a. 15

Step 1: Find ALL factor pairs that when multiplied will give a product of 15. Check numbers 1-10 as possible factors using division (÷) if necessary. 15

1 15

3 5


Example 1) cont’d.

a. 15

Step 2: Decide if the number is prime or composite based on the number of factors listed. 15 has 4 factors, so it must be composite.

Write: 15: 1, 3, 5, 15 COMPOSITE__


Example 1) cont’d: Find all the factors of the numbers below and classify them as prime or composite numbers.

b) 17: ________________________ c) 48: _________________________ d) 57: __________________________


Example 1) cont’d: Find all the factors of the numbers below and classify them as prime or composite numbers.

b) 17 : 1, 17, prime__________ c) 48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, composite d) 57 : 1, 57, prime__________


Example 2) Find the prime factorization of the number below using the factor tree method.

a) Step 1: Draw the factor tree with the number at the top. Step 2: Use the prime cloud numbers to start factoring (ex. 2, 3, 5, 7, 11…) or start with a factor pair of the number. Step 3: Factor all composite numbers until you have all prime numbers circled. Step 4: Check your prime factorization using multiplication. Order the numbers from smallest to largest.

Prime Factorization of 44: 2 x 2 x 11

11 4

2 2



b)

Prime Factors of 16: x x x



b)

Prime Factors of 16: 2 x 2 x 2 x 2



b)

Prime Factors of 42: x x



b)

Prime Factors of 42: 2 x 3 x 7


Example 3) Find all the common factors and the GCF of the numbers below.

REMEMBER: The Greatest Common Factor is the BIGGEST factor the numbers both have!

First, list all of the factors for each of the numbers.

Factors of 20 ________________________ Factors of 24 _________________________


Example 3) Find all the common factors and the GCF of the numbers below. REMEMBER: The Greatest Common Factor is the BIGGEST factor the numbers both have!

Factors of 20 __:_1, 2, 4, 5, 10, 20, Factors of 24 ____:__1, 2, 3, 4, 6, 8, 12, 24,


Draw a Venn Diagram.


Step 1: Write each number above the left or right circle of the Venn Diagram. Label “Common” for the shared space in the middle.

20 Common 24


Step 2: Factor both numbers. Find ALL factors for each number and write the factors in the Venn Diagram. Step 3: Circle all the factors that are the same on both circles in the Venn Diagram.Step 4: Write ALL of the common factors in the shared space in the middle. Step 5: Out of the common factors, identify the BIGGEST factor. Circle it and label as your GCF.

20 Common 24

Reasoning Mind Academy: “Now, it’s your turn to try!”

Independent Practice Problems

Helpful Hints:Read the problem twice.Underline any important parts.Make a plan for solving the problem.Show your work,Do your best!

common factors *identify common factors of a set of whole numbers 5.3d *identify prime &...

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common factors identify common factors of a set of whole numbers 5.3d identify prime &...