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 & Composite Numbers using Patterns in Factor Pairs 5.5B
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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)
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Reasoning Mind Academy: Common Factors
REMEMBER: A product is the answer to a multiplication problem.
Key Words:
prime composite factors
product factor pairs
prime factorization common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
Definition: are numbers that are multiplied together to get a product.
Key Words:
prime composite(2) factors
product factor pairs
(prime factorization) common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
Definition: Factors are numbers that are multiplied together to get a product.
Key Words: prime composite factors
product factor pairs(prime factorization) common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
REMEMBER: Factor x Factor = Multiple or Product
Example: (Factor) 7 x (Factor) 11 = (Product) 77
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Reasoning Mind Academy: Common Factors
Definition: A number is a whole number that has only two factors: one and the number itself.
Key Words:
prime composite(2) factors
product factor pairs
(prime factorization) common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
Definition: A prime number is a whole number that has only two factors: one and the number itself.
Key Words:
prime composite factors
product factor pairs
(prime factorization) common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
Definition: A number is a whole number that has three or more factors.
Key Words:
prime composite(2) factors
product factor pairs
(prime factorization) common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
Definition: A composite number is a whole number that has three or more factors.
Key Words:
prime composite factors
product factor pairs
(prime factorization) common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
REMEMBER: numbers can be odd OR even.
Key Words:
prime composite(2) factor
product factor pairs
(prime factorization) common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
REMEMBER: Composite numbers can be odd OR even.
Key Words:
prime composite factor
product factor pairs
(prime factorization) common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
REMEMBER: is special! It is neither prime nor composite!
Which Number????
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Reasoning Mind Academy: Common Factors
REMEMBER: One is special! It is neither prime nor composite!
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Reasoning Mind Academy: Common Factors
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
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
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
product factor pairsprime factorization common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
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
product factor pairs
prime factorization common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
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
product factor pairsprime factorization common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
REMEMBER: means to “factor”, “fracture”, or “break down” numbers.
Key Words: prime composite(2) factor
product factor pairsprime (factorization) common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
REMEMBER: Factorization means to “factor”, “fracture”, or “break down” numbers.
Key Words:
prime composite factor
product factor pairs
prime (factorization) common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
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
Key Words: prime composite factor
product factor pairsprime factorization common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
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
Key Words: prime composite factor
product factor pairsprime factorization common factor
Greatest Common Factor (GCF)
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Reasoning Mind Academy: Common Factors
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 composite factor
product factor pairs
prime factorization common factors
Greatest Common Factor
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Reasoning Mind Academy: Common Factors
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 composite factor
product factor pairs
prime factorization common factors
Greatest Common Factor
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Reasoning Mind Academy: Common Factors
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
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Reasoning Mind Academy: Common Factors
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
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Reasoning Mind Academy: Common Factors
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__
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Reasoning Mind Academy: Common Factors
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: __________________________
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Reasoning Mind Academy: Common Factors
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__________
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Reasoning Mind Academy: Common Factors
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
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Reasoning Mind Academy: Common Factors
Example 2) Find the prime factorization of the number below using the factor tree method.
b)
Prime Factors of 16: x x x
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Reasoning Mind Academy: Common Factors
Example 2) Find the prime factorization of the number below using the factor tree method.
b)
Prime Factors of 16: 2 x 2 x 2 x 2
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Reasoning Mind Academy: Common Factors
Example 2) Find the prime factorization of the number below using the factor tree method.
b)
Prime Factors of 42: x x
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Reasoning Mind Academy: Common Factors
Example 2) Find the prime factorization of the number below using the factor tree method.
b)
Prime Factors of 42: 2 x 3 x 7
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Reasoning Mind Academy: Common Factors
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 _________________________
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Reasoning Mind Academy: Common Factors
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,
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Reasoning Mind Academy: Common Factors
Draw a Venn Diagram.
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Reasoning Mind Academy: Common Factors
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
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Reasoning Mind Academy: Common Factors
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
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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!