Prime Numbers and Greatest Common Factor GCF

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Prime NumbersandGreatest Common Factor (GCF)
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Definitions
Factors Numbers that are multiplied together to
obtain another number.
(3 and 7 are factors of the number 21.)
Prime Numbers A natural number that has only two
factors (1 and itself).
Composite Numbers Numbers that are not prime,
but are instead created by multiplying a
combination of prime numbers.
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Prime Factorization
To write the prime factorization of a number,
write the number as a product of prime numbers.
Prime Factorization 2 2 2 3 or 23
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Prime Factorization
Prime Factorization 2 2 2 2 7 or
24 7
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Prime Factorization
Prime Factorization 2 149
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Prime Factorization
48
Prime Factorization 2 2 2 2 3 or
24 3
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Prime Factorization
Factor the expression completely. Do not use
exponents.
12x2y
Prime Factorization 2 2 3 x x y
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Prime Factorization
Factor the expression completely. Do not use
exponents.
-24x2y3z
Prime Factorization -2 2 2 3 x x
y y y z
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Definitions
Common Factor of Two Natural Numbers A number
that is a factor of both numbers.
Greatest Common Factor (GCF) The largest number
that is a factor of both.
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Greatest Common Factor
Find the GCF of 24 and 100.
24
100
2 2 2 3
2 2 5 5
GCF is 2 2 4
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Greatest Common Factor
Find the GCF of 48 and 90.
48
90
2 2 2 2 3
2 3 3 5
GCF is 2 3 6
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Greatest Common Factor
Find the GCF of 200 and 500.
200
500
2 2 2 5 5
2 2 5 5 5
GCF is 2 2 5 5 100
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Greatest Common Factor
Find the GCF of 6x2y and 12xy.
6x2y
12xy
2 3 x x y
2 2 3 x y
GCF is 2 3 x y 6xy
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Greatest Common Factor
Find the GCF of 36x2yz and 48x4z.
36x2yz
48x4z
2 2 3 3 x x y z
2 2 2 2 3 x x x x z
GCF is 2 2 3 x x z 12x2z