Honor's Pre­Algebra ­ Prime Factorization (Chapter 4­2)
Prime Factorization
(Honor’s Pre-Algebra)
Prime Number: A whole number
that has exactly two different factors
(1 and itself).
Composite Number: A whole
number that has three or more
different factors.
Monomial: A number, variable,
or a product of numbers and variables.
Determine whether each number
is prime, composite, or neither.
1. 47
2. 57
3. 0
4.
Find the Prime Factorization
using any method.
1.) 144
2.) 108
Factor each monomial.
1.) 28ab2
2.) -36x2y2
Prime Factorization à Breaking a
number into all prime factors being
multiplied together.
Write these factors from least to
greatest.
• To check: Your answer, when
multiplied, should be equal to the
original number.
Factor Tree
• Find two factors (neither being 1)
and bring them down a line and
multiply them.
• Determine if either of those factors
can break down to smaller factors.
• If so, repeat the process.
Continue this process until all of
the factors are prime.
• To check: multiply the prime
factors (the Prime factorization)
and your answer should be the
same as the original number.
Division Steps
• Divide the original number by a
prime factor and place your
quotient on top of the step.
• If the quotient is composite,
divide it by another prime factor
and follow the previous step.
• Repeat these steps until the
quotient is prime.
• At this time, line up all of the
prime factor to multiply and
you have the prime factorization.
Factor each monomial.
• Find the prime factorization of each
number and write using factors.
• Write the variables as factors of the
exponent.
• If the monomial is negative, multiply
the prime factorization by -1.
3.) 24ab2c3
1
Honor's Pre­Algebra ­ Prime Factorization (Chapter 4­2)
Prime Factorization
(Honor’s Pre-Algebra)
Prime Number: A whole number
that has exactly two different factors
(1 and itself).
Composite Number: A whole
number that has three or more
different factors.
Monomial: A number, variable,
or a product of numbers and variables.
Determine whether each number
is prime, composite, or neither.
1. 47
2. 57
3. 0
4.
Find the Prime Factorization
using any method.
1.) 144
2.) 108
Factor each monomial.
1.) 28ab2
2.) -36x2y2
Prime Factorization à Breaking a
number into all prime factors being
multiplied together.
Write these factors from least to
greatest.
• To check: Your answer, when
multiplied, should be equal to the
original number.
Factor Tree
• Find two factors (neither being 1)
and bring them down a line and
multiply them.
• Determine if either of those factors
can break down to smaller factors.
• If so, repeat the process.
Continue this process until all of
the factors are prime.
• To check: multiply the prime
factors (the Prime factorization)
and your answer should be the
same as the original number.
Division Steps
• Divide the original number by a
prime factor and place your
quotient on top of the step.
• If the quotient is composite,
divide it by another prime factor
and follow the previous step.
• Repeat these steps until the
quotient is prime.
• At this time, line up all of the
prime factor to multiply and
you have the prime factorization.
Factor each monomial.
• Find the prime factorization of each
number and write using factors.
• Write the variables as factors of the
exponent.
• If the monomial is negative, multiply
the prime factorization by -1.
3.) 24ab2c3
2
Honor's Pre­Algebra ­ Prime Factorization (Chapter 4­2)
Prime Factorization
(Honor’s Pre-Algebra)
Prime Number: A whole number
that has exactly two different factors
(1 and itself).
Composite Number: A whole
number that has three or more
different factors.
Monomial: A number, variable,
or a product of numbers and variables.
Determine whether each number
is prime, composite, or neither.
1. 47
2. 57
3. 0
4.
Find the Prime Factorization
using any method.
1.) 144
2.) 108
Factor each monomial.
1.) 28ab2
2.)
-36x2y2
Prime Factorization à Breaking a
number into all prime factors being
multiplied together.
Write these factors from least to
greatest.
• To check: Your answer, when
multiplied, should be equal to the
original number.
Factor Tree
• Find two factors (neither being 1)
and bring them down a line and
multiply them.
• Determine if either of those factors
can break down to smaller factors.
• If so, repeat the process.
Continue this process until all of
the factors are prime.
• To check: multiply the prime
factors (the Prime factorization)
and your answer should be the
same as the original number.
Division Steps
• Divide the original number by a
prime factor and place your
quotient on top of the step.
• If the quotient is composite,
divide it by another prime factor
and follow the previous step.
• Repeat these steps until the
quotient is prime.
• At this time, line up all of the
prime factor to multiply and
you have the prime factorization.
Factor each monomial.
• Find the prime factorization of each
number and write using factors.
• Write the variables as factors of the
exponent.
• If the monomial is negative, multiply
the prime factorization by -1.
3.) 24ab2c3
3
Honor's Pre­Algebra ­ Prime Factorization (Chapter 4­2)
4
Honor's Pre­Algebra ­ Prime Factorization (Chapter 4­2)
5
Honor's Pre­Algebra ­ Prime Factorization (Chapter 4­2)
6
Honor's Pre­Algebra ­ Prime Factorization (Chapter 4­2)
Prime Factorization
(Honor’s Pre-Algebra)
Prime Number: A whole number
that has exactly two different factors
(1 and itself).
Composite Number: A whole
number that has three or more
different factors.
Monomial: A number, variable,
or a product of numbers and variables.
Determine whether each number
is prime, composite, or neither.
1. 47
2. 57
3. 0
4. 51
Find the Prime Factorization
using any method.
1.) 144
2.) 108
Factor each monomial.
1.) 28ab2
Prime Factorization à Breaking a
number into all prime factors being
multiplied together.
Write these factors from least to
greatest.
• To check: Your answer, when
multiplied, should be equal to the
original number.
Factor Tree
• Find two factors (neither being 1)
and bring them down a line and
multiply them.
• Determine if either of those factors
can break down to smaller factors.
• If so, repeat the process.
Continue this process until all of
the factors are prime.
• To check: multiply the prime
factors (the Prime factorization)
and your answer should be the
same as the original number.
Division Steps
• Divide the original number by a
prime factor and place your
quotient on top of the step.
• If the quotient is composite,
divide it by another prime factor
and follow the previous step.
• Repeat these steps until the
quotient is prime.
• At this time, line up all of the
prime factor to multiply and
you have the prime factorization.
Factor each monomial.
• Find the prime factorization of each
number and write using factors.
• Write the variables as factors of the
exponent.
• If the monomial is negative, multiply
the prime factorization by -1.
2.) -36x2y2
3.) 24ab2c3
7
Honor's Pre­Algebra ­ Prime Factorization (Chapter 4­2)
8