This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

- Welcome
- Learning Math Strategies (Online)Toggle Dropdown
- Study Skills for MathToggle Dropdown
- Simply Math
- Business MathToggle Dropdown
- How to use a scientific calculator
- Place Value in Decimal Number Systems
- Arithmetic Operations
- Basic Laws
- Operations on Signed numbers
- Order of Operations
- Fractions
- Decimals
- Percents
- Ratios and Proportions
- Exponents
- Statistics
- Factoring
- Rearranging Formulas
- Solving Linear Equations
- Solving Systems of Linear Equations
- Trade and Cash Discounts
- Multiple Rates of Discount
- Payment Terms and Cash Discounts
- Markup
- Markdown
- Simple Interest
- Equivalent Values
- Compound Interest
- Equivalent Values in Compound Interest
- Nominal and Effective Interest Rates
- Ordinary Simple Annuities
- Ordinary General Annuities

- Hospitality MathToggle Dropdown
- Place Value in Decimal Number Systems
- Arithmetic Operations
- Order of Operations
- Basic Laws
- Prime Factorisation and Least Common Multiple
- Fractions
- Decimals
- Percents
- Exponents
- Units of Measures
- Fluid Ounces and Ounces
- Metric Measures
- Yield Percent
- Recipe Size Conversion
- Ingredient Ratios
- Food-Service Industry Costs

- Engineering MathToggle Dropdown
- Basic Laws
- Order of Operations
- Prime Factorisation and Least Common Multiple
- Fractions
- Exponents
- Radicals
- Reducing Radicals
- Factoring
- Rearranging Formulas
- Solving Linear Equations
- Areas and Volumes of Figures
- Congruence and Similarity
- Functions
- Domain and Range of Functions
- Basics of Graphing
- Transformations
- Graphing Linear Functions
- Graphing Quadratic Functions
- Solving Systems of Linear Equations
- Solving Quadratic Equations
- Solving Higher Degree Equations
- Trigonometry
- Graphing Trigonometric Functions
- Graphing Circles and Ellipses
- Exponential and Logarithmic Functions
- Complex Numbers
- Number Bases in Computer Arithmetic
- Linear Algebra
- Calculus
- Set Theory
- Modular Numbers and Cryptography
- Statistics
- Problem Solving Strategies

- Upgrading / Pre-Health
- Basic Laws
- Place Value in Decimal Number Systems
- Decimals
- Significant Digits
- Prime Factorisation and Least Common Multiple
- Fractions
- Percents
- Ratios and Proportions
- Exponents
- Radicals
- Reducing Radicals
- Metric Conversions
- Factoring
- Solving Linear Equations
- Solving Quadratic Equations
- Functions
- Domain and Range of Functions
- Polynomial Long Division
- Exponential and Logarithmic Functions
- Statistics

- Nursing MathToggle Dropdown
- Arithmetic Operations
- Order of Operations
- Place Value in Decimal Number Systems
- Decimals
- Fractions
- Percents
- Ratios and Proportions
- Nutrition Labels
- Interpreting Drug Orders
- Oral Dosages
- Dosage Based on Size of the Patient
- Parenteral Dosages
- Intravenous (IV) Administration
- Infusion Rates for Intravenous Piggyback (IVPB) Bag
- General Dosage Rounding Rules

- Transportation MathToggle Dropdown
- PhysicsToggle Dropdown
- Architectural MathToggle Dropdown

A **prime number** is a number that is only divisible by 1 and itself. Below is a list of the first 15 prime numbers:

\[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47\]

Every number can be written as a product of prime numbers. For example,

\[6=2 \times 3\]

\[8 = 2 \times 2 \times 2 \text{ or } 2^3\]

\[21 = 3\times 7\]

In the above examples,

- \(2 \times 3\) is the prime factorisation of \(6\),
- \(2\times 2\times 2\) is the prime factorisation of \(8\),
- \(3\times 7\) is the prime factorisation of \(21\).

There may be times when you are asked to find the prime factorisation of a number, but the number is very large. See the video below for an example of finding the prime factorisation of a large number.

The **Least Common Multiple **of a group of numbers is the smallest number that is divisible by all of the numbers in the group.

For example, let's try to find the least common multiple of the numbers \(2,3\) and \(4\) - i.e., we want to find the smallest number that is divisible by \(2,3\) and \(4\).

Let's look at the multiples of each of the numbers and identify the first one that is common to all three:

- Multiples of \(2\): \(2,4,6,8,10,\)\(12\),\(14,16,18,20\)
- Multiples of \(3\): \(3,6,9,\)\(12\),\(15,18,21\)
- Multiples of \(4\): \(4,8,\)\(12\),\(16,20,24\)

The smallest number that is in all of the lists is the least common multiple - \(12\).

Writing out the list of multiples and comparing lists is a valid way to find the least common multiple, but this can be difficult if the numbers get large or the lists get long. There is also a method to finding the least common multiple using the prime factorisation of each of the numbers.

- Write down the prime factorisation of each of the numbers.
- Multiply each factor together the greatest number of times it appears in each prime factorisation.

**Example: **Find the least common multiple of \(8,9\) and \(12\).

Let's start by writing the prime factorisations of each:

- \(8 = 2\times 2\times 2\)
- \(9 = 3\times 3\)
- \(12 = 2\times 2\times 3\)

The only prime numbers present in the prime factorisations are \(2\) and \(3\). The greatest number of times \(2\) appears in the above factorisations is three times (in \(8\)) and the greatest number of times \(3\) appears is twice (in \(9\)). Therefore, the least common multiple is

\[2\times 2\times 2\times 3\times 3 = 72\]

so \(72\) is the least common multiple of \(8,9\) and \(12\). As an exercise, verify this by writing out all the multiples of \(8,9\) and \(12\) and finding the smallest number in each of the lists - i.e., complete the lists below:

- Multiples of \(8\): \(8,16,24,\) ...
- Multiples of \(9\): \(9,18,27,\) ...
- Multiples of \(12\): \(12,24,36,\) ...

The product of two numbers is the number you get when you multiply the numbers. For example, the product of \(4\) and \(5\) is \(20\).**Product:**A factor of a number is a number that divides in evenly. For example, factors of \(20\) are \(1\), \(2\), \(4\), \(5\), \(10\) and \(20\) because all of those numbers divide in to \(20\), with no remainder.**Factor:**A factorisation of a number is a is what you get when you break a number up into a product of other numbers. For example, \(4 \times 5\) is a factorisation of \(20\). So is \(2 \times 10\).**Factorisation:**A number \(A\) is divisible by another number \(B\) if \(B\) divides into \(A\) without a remainder. For example, \(20\) is divisible by \(4\) because \(4\) divides into \(20\) \(5\) times with no remainder.**Divisible:**A multiple of a number is that number multiplied by a whole number. For example, \(20\) is a multiple of \(5\) because it is \(5 \times 4\). To check if a number \(A\) is a multiple of \(B\), divide \(B\) into \(A\) and see if there is a remainder. If there is no remainder, then it is a multiple.**Multiple:**

- Last Updated: Jul 18, 2024 3:28 PM
- URL: https://libraryguides.centennialcollege.ca/mathhelp
- Print Page

chat loading...