Page 168 - ABCTE Study Guide_Neat

Prime factorization is the process that finds the prime-number products of a given composite number.
Prime factorization is useful in its own right, but many of the applications for it involve fractions, which we’ll
cover down the road.

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You may be able to find a number’s prime factorization in your head. For example, 12 is 2 x 2 x 3 or 2 x
3. (Prime factorizations are often represented with exponents.)

If you can’t find the prime factorization mentally, try either a Factor-T or a Factor Tree.

Review:

• Prime numbers have exactly two factors, one and itself.
• Composite numbers have more than two factors but not an infinite number..
• Zero and one are neither prime nor composite.
• Divisibility rules are shortcuts that can assist you in determining factors of a number.
• Every composite number can be written as a unique product of prime numbers, which is
called a number’s prime factorization.
• Two handy methods of finding prime factorizations are factor-T’s and factor trees.

Calculating with Rational Numbers

Lesson Objective

In this lesson we will review positive and negative integers.

Previously Covered

• In the sections above, we discussed prime numbers and the fact that they have exactly
two factors: the number one and the number itself.
• We also covered the divisibility rules (shortcuts to tell you if one number is divisible by
another number) and the idea of prime factorization, which is the process that finds the
prime-number products of a given composite number.

Those Pesky Negative Numbers

We know, we know: This is why calculators were invented. But let’s stay positive—so to speak.

We’ll start with integers, rather than fractions and decimals, because the rules are all the same, and
integers are easier to add, subtract, multiply, and divide mentally.

Test Yourself:

Question

Solve x = –19 + 41.

A x = –60