Study Guide
Factors and Greatest Common Factor
If two or more numbers are multiplied, each number is a factor of the product.
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Definition |
Example |
Prime Number |
A prime number is a whole number, greater than 1, whose only factors are 1 and itself |
5 |
Composite Number |
A composite number is a whole number, greater than 1, that is not prime. |
10 |
Prime Factorization |
Prime factorization occurs when a whole number is expressed as a product of factors that are all prime numbers. |
45 = 32 · 5 |
Greatest Common Factor (GCF) |
The greatest common factor of two or more integers is the greatest number than is a factor of the integers. |
The GCF of 12 and 30 is 6 |
The GCF of two or more monomials is the product of their common factors, when each monomial is expressed in factored form.
Directions: State whether each number is prime or composite.
If the number is composite, find its prime factorization. |
28 composite
22 · 7 |
61 prime |
112 composite
24 · 7 |
2865 composite
3 · 5 · 191 |
Directions: Factor each expression completely. Do NOT use exponents. |
−34 −1 · 2 · 17 |
−150 −1 · 2 · 3 · 5 · 5 |
56pq3 2 · 2 · 2 · 7 · p · q · q · q |
−108(cd)2 −1 · 2 · 2 · 3 · 3 · 3 · c · c · d · d |
Directions: Find the GCF of the given monomials. |
−45, 15 15 |
169, 13 13 |
−20, 440 20 |
49x, 343x2 49x |
4a7b, 28ab 4ab |
97y, 12x, −8y 8 |
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