# Factors of Integers Worksheets

A factor is a number that divides into another number evenly without any remainder. Factors are always less than or equal to the given number. This primarily requires us to rely on the operations of division and multiplication. Make sure that your skills are sharp with those operations before you jump headfirst into this topic. We will show two different common methods to find factors of integers. Guess which operations that they are centered around? These worksheets and lessons not only show you how to find all the factors of an integer, but also what to do with them. This skill will come in handy when we begin to need to reduce and simplify equations and algebraic expressions.

### Aligned Standard: 6.NS.B.4

- Factor 9 Please Step-by-Step Lesson- Yes, this is just as advertised!
- Guided Lesson - We look for all the factors of a number, the greatest common factor, and a word problem.
- Guided Lesson Explanation - These can all be done in three steps.
- Practice Worksheet - Sorry, that I spent more time on working on factors.
- Matching Worksheet - A nice helping of the three core skills this standard addresses.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

We work on common multiples, factors, and greatest factors.

- Homework 1 - Whole numbers that can be used to form a product are factors of that product. There can be many different combinations of factors.
- Homework 2 - Every non-zero number divides evenly into itself and 1.
- Homework 3 - A number has factors including 3 and 4. What other number must also be a factor of the same number?

### Practice Worksheets

These seem to be part brain teaser for kids. Help them organize their thoughts with these.

- Practice 1 - If two factors have a common multiple than that number is also a factor.
- Practice 2 - Find the greatest common factor of 15 and 25.
- Practice 3 - Keep going until there are no other numbers that divide into evenly into your value.

### Math Skill Quizzes

Remind students to read these problem carefully. The context might trip them up.

- Quiz 1 - Find all the factors of 27.
- Quiz 2 - A number has factors including 4 and 16. What other number must also be a factor of the same number?
- Quiz 3 - See what you know and what you don't.

### How to Determine the Factors of an Integer

Factoring an integer despite popular belief is a very easy process. To successfully do it, you need to simply break the integer into groups of numbers whose product is equal to its original number. Factors are separated using a multiplication sign. Remember, 1 is the factor for every single integer and all factors of that number can be evenly divided into that number. If the number is even 2 is one of the factors that can be found. Do you see how this aligns itself with the rules of divisibility?

**Division Method** - This method reminds me of throwing darts at a board with random accuracy, hence the picture. It starts with you finding all the numbers less than or equal your starting value. You then divide these number into this value to see which create a quotient with no remainder.

**Multiplication Method** - I favor this method simply because it is more intuitive and students often spend a great deal of time with their times tables, which fits in here perfectly. You simply write all the numbers that when taken as products form this value. Ever value that is involved in producing this product is therefore a factor.

Examples, Let's factor the number 3 - {3 x 1 = 3} Factors of 3 are 3 and 1. Factor number 10 - Since 10 can be written as 5 x 2 x 1, the factor of the number 10 is 10, 5, 2, and 1. The number 10 can be divided into 10, 5, 2, and 1. Factor the number 18 - Number 18 can be written as 18 x1 or 9 x 2 x 1 or 6 x 3 x 1 or 3 x 3 x 2 x 1. Since 18 can be divided by 18, 9, 6, 3, 2, and 1 and then 18, 9, 6, 3, 2, and 1 are its factors.