Factors Number Theory
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Factors & Number Theory
Grade 6
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Factors A whole number that divides exactly into
another whole number is called a factor of that number. • For example: 100 / 25 = 4
• So, 25 is a factor of 100 as it divides exactly into 20.• 20 / 4 = 5• So, 4 is a factor of 20 as it divides exactly into 20.
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We divide 22 by 7 and check if remainder is zero 37 ) 22 21 1
As the remainder is 1 we conclude that 7 is not a factor of 22.
How do we check if a number is a factor of another number Is 7 a factor of 22?
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Find the factors of 20
List all the factors of 35.
Try This!
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The exponent is sometimes referred to as the power.
46 BaseExponent
Powers and Exponents
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46 means to multiply the base 4 by itself 6 times
46 = 4 x 4 x 4 x 4 x 4 x 4
However we must remember that
40 = 1
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3 x3 + 5 y2 =
3.5x2 y3 - xy2 =
Where x = (-2) and y = (-3)
Try This!
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A Prime number is a positive integer A Prime number is a positive integer >1>1
A number that has exactly two factors, A number that has exactly two factors, 1 and itself1 and itself
A number that cannot be A number that cannot be factored .factored .7 is a Prime number as it has only two factors 1 and 7
Prime Numbers
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When a whole number greater than one has more than 2 factors it is called a Composite Number.
10 is a composite number as it has 1, 2, 5 and 10 as its factors
Composite Numbers
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Expressing a composite number as a Expressing a composite number as a product of prime numbers is called Prime product of prime numbers is called Prime FactorizationFactorization
When we express a number as a product of prime factors, we have actually factored it completely. We refer to this process as prime factorization
The number 60 is a composite number. It can be written as the product 2 x 2 x 3 x 5. Note that 2, 3 and 5 are factors of 60 and all these factors are prime numbers. We call them prime factors.
Prime Factorization
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460460
10 * 4610 * 46
2 * 5 23 * 22 * 5 23 * 2
460 =460 = 2 * 2 * 5 * 232 * 2 * 5 * 23
Prime factors of 460 are Prime factors of 460 are 2² * 5 * 232² * 5 * 23
Methods for finding Prime Factorization
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56 =
24 =
Try This! Find out the Prime Factors of the
following
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Greatest Common Factor Greatest Common Factor of two or more
numbers can be defined as the greatest number that is a factor of each number
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Greatest Common Factor Method 1:
• List the factors of each number. Then identify the common factors. The greatest of these common factors is the GCF.
Method 2:• Write the prime factorization of each number.
Then identify all common prime factors and find their product.
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Greatest Common Factor Find the GCF of 27 and 36 Method 1:
• List all the factors of both the numbers • Factors of 27 : 1, 3, 9, 27
• Factors of 36 : 1, 2, 3, 4, 6, 9, 12, 18, 36
• Thus, the GCF of 27 and 36 is 9
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Write the prime factorization of 27 and 36
27 36
3 x 9 3 x 12
3 3 x 3 3 x 4
3 3 2 x 2
Method 2
Common Prime factors are 3 x 3 = 9
Greatest Common Factor
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1)160 and 550
2) 20a2 and 14ab
3) 36, 24, 144, 96
Try This! Find GCF of the following set of numbers
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Lets take a Break !
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Title: Format: WebEx Web BrowserDouble-click to edit
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Least Common Multiple The least common multiple of the
numbers a and b is the smallest number that is divisible by both a and b.
We denote the least common multiple of a and b by LCM (a, b).
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List several multiples of each number. Then identify the common multiples. The least of these is the LCM.
Method 1
Multiples of 6 : 6, 12, 18, 24, 30,36,…
Multiples of 9 : 9, 18, 27, 36, 45, 54, 63,...
As 18 is the least number which is a common multiple hence
LCM of 6 and 9 is 18
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Find the prime factors of each number, then identify all common prime factors. For each prime factor, write it down the greatest number of times it appears in any of the numbers. The product is the LCM
Method 2
9 = 3 x 3 = 32
12 = 2 x 2 x 3 = 22 x 3
15 = 3 x 5
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The prime factors are 2, 3 and 5. The greatest number of times 2 appears is twice (in 12), So we write it down twice. The greatest number of times 3 appears is twice (in 9), so we again write it down twice. The greatest number of times 5 appears is once (in 15), so write it down once. The LCM of 9, 12 and 15 is
2 x 2 x 3 x 3 x 5 = 180
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Find the LCM of the following
1) 56 and 16
2) 3, 7, 14
3) 29, 58, 4
Try This!
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1) Express the smallest five digit number in the form of prime numbers
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2) Diana is thinking of two numbers The GCF is 6 and the LCM is 36. If one of the number is 12, what is the other number?
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3) The product of any three consecutive numbers is always divisible by 6. Comment.
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Great Job Done! Be sure to practice what you have
learned today!!!
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