Prime factorization

We know for a fact that there are a lot of numbers, there are whole numbers, fraction, decimal, radicals, irrational numbers, integers, complex numbers and more. In this chapter we will take a look at all the 4 different number systems namely, the natural numbers, whole numbers, rational numbers and irrational numbers.

In 3.1, we will be looking studying the differences between these numbers systems. In this chapter we will be dwelling with the real numbers. First, we will be learning about Natural Numbers. These are basically all the numbers that are either a positive or negative integer. Second, is the whole numbers, which pertains to all numbers that are whole like 5, 17, 233 etc. Second would be the Whole numbers which are basically natural numbers that are either positive integers or zero. Third would be the real numbers which comprises the rational numbers, which we tackled in the chapter on rational numbers in earlier grade. Fourth would be the Irrational numbers which are the opposite of rational numbers.

In 3.2 we will be learning how to factor out a number. This is very useful in so many math problems specifically in simplifying equations. We will be looking at the definition Prime numbers, Composite numbers, and the factor Tree which are important for us to learn and understand how to do the prime factorization. In the proceeding parts we will be learning about Greatest Common factor, Least Common multiples which are also very important to factor a certain number.

In 3.5 we will take a closer look at the rational and irrational numbers. We will have exercises that will help us identify them and also to order them in the number line. Lastly, in 3.6 we will be reviewing concepts we previously learned regarding Fractions, Decimals and Percentages, specifically converting them from one form to another.

Prime factorization

A prime number is a whole number which can only be divided evenly by one or itself. Composite numbers are whole numbers that is not prime or has more than 2 factors. Prime factorization is a process that looks for prime factors of a number.


Factor : Numbers that can be multiplied together to give the original value
Ex: The factor of 15 is 5 & 3. Because 5×3=155 \times 3 = 15

Prime numbers : A whole number that has only "two" factors: 1 & itself.
Ex: 2,3,5,7,11,13,17…

Composite numbers : A Whole number that is not prime or has more than 2 factors.
Ex: 4,6,8…

Zero & One : They are neither primer nor composite

Factor Tree : A method of finding prime factors by using a tree diagram.
Ex: Prime factors of 18 = 2×3×3 2 \times 3 \times 3

: A method of finding prime factors by using a continuous division.
Ex: Prime factors of 72 = 2×2×2×3×3 2 \times 2 \times 2 \times 3 \times 3

  • 2.
    Determine if the numbers are prime or composite.
  • 3.
    What are the prime factors of the following numbers?
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Prime factorization

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