Study Guide: Factors and Greatest Common Factor

These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 textbook (Glencoe Algebra 1 — ISBN: 9780028253282) into html format.

Study Guide
Factors and Greatest Common Factor

If two or more numbers are multiplied, each number is a factor of the product.

	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.

composite
2² · 7

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

169, 13

−20, 440

49x, 343x²

49x

4a⁷b, 28ab

4ab

97y, 12x, −8y