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Purcell Math

Math Methods Grades 4-8

Factors, Prime Numbers, and Prime Factorization

Introduction

Understanding factors, prime numbers, and prime factorization is essential to mastering number sense in mathematics. Here’s a quick guide to help clarify each concept:

Core Skills

1. Factors
Factors of a number are numbers that, when multiplied together, produce that number.

Example: The factors of 12 are 4 and 3, since:

\[ 4 \times 3 = 12 \]

Example: The factors of 24 include 4 and 6, because:

\[ 4 \times 6 = 24 \]

2. Prime Numbers
A prime number has exactly two factors: 1 and itself.

Examples:

\[ 2 \] is prime because \[ 2 \times 1 = 2 \] and there are no other factors.
\[ 3 \] is prime because \[ 3 \times 1 = 3 \] and there are no other factors.

3. Prime Factorization
Prime factorization is breaking down a number into a product of prime numbers.

Example: The prime factorization of 12 is:

\[ 12 = 2 \times 2 \times 3 \] where \[2\] and \[3\] are prime numbers.

4. Identity Number
The number 1 is called the identity number because multiplying any number a by 1 gives a:

\[ a \times 1 = a \]

Conclusion

Mastering these concepts will help in solving a variety of math problems. Keep practicing to build confidence in working with factors and prime numbers!

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