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What numbers can be multiplied together to get 24?
1 x 24
2 x 12
3x8
4x6
The number 24 is called the product because it is the
result of multiplying two or more numbers together.
The numbers 1, 2, 3, 4, 6, 8, 12, and 24 are called
factors. These are the numbers being multiplied
together.
What are the factors of seven?
1x7
Composite numbers – numbers which have two or more
factors like the number 24.
Prime numbers – numbers having exactly two factors: one
and itself. Seven is a prime number.
Factor 56 using only prime factors.
To do this, we can make a factor tree as follows.
56
2 is prime.
2
2 is prime.
2 is prime.

2
28 is composite so we can
factor it further.
28
 14
2

14 is composite, so we can
factor it further.
7
7 is prime.
The prime factorization of 56 is 2  2  2  7 or 23 
7.
or
We can make a factor tree using different starting factors.
56
4 is composite
so we can factor
it further.
4
2

14 is composite so we can
factor it further.

2
14
2
 7
2 is prime.
7 is prime.
The prime factorization of 56 is 2  2  2  7 or 23 
7.
The prime factorization of every number is unique. No
matter what factors you choose, the prime factorization will
still be the same for that number.
Find the prime factorization of the following two numbers.
60
2
105
 30
2
 15
5
 21
3
 7
60 = 2  2  3 
3  5
5.105 = 3  5 
7
What factors do these two numbers have in common?
The greatest common factor of 60 and 105 is 3  5 or
15.
3 and 5
Find the greatest common factor (GCF) of the given monomials.
1. 34, 85
2. 14p4q, 35pq3
3. 15x2, 30xy2, 57x3y
Determine whether each number is prime or composite. If the
number is composite, find its prime factorization.
4. 145
5. 113
6. To find the area of a rectangle, you multiply length
times width. If a rectangle has an area of 124 square
inches, what are its possible dimensions?
1) 34 = 2  17
85 = 5  17
The greatest common factor (GCF) of
34 and 85 is 17.
2) 14p4q = 2  7  p  p  p  p The GCF is 7pq .
q
35pq3 = 5  7  p  q  q  q
3) 15x2 = 3  5  x  x
30xy2 = 2  3  5  x  y
y
57x3y = 3  19  x  x  x
y
The GCF is 3x .
4. 145 is composite.
145 = 5  29
5.
113 is a prime number.
The area of a rectangle is the product of two factors.
The factors of 124 are:
1 x 24
2 x 62
4 x 31
Therefore, the possible dimensions of the rectangle are
1 in. x 124 in.
2 in. x 62 in.
4 in. x 31 in.