# Factor Pairs to 100 Worksheets

At this level we begin to ponder the various ways that numbers can be built from multiplication operations. Students often confuse the concept of factors and multiples at this level. Factors are all the values that you can divide evenly (no remainders) into a number. An example of a factor would be the factors of 14: 1, 2, 7, 14. These factor values come in pairs meaning that those are the two values that when multiplied are equal to product we are looking for. For example, for 14 the pairs are 1 and 14, 2 and 7. Multiples on the other hand are values that can be divided evenly by that number. For example the first 5 multiples of 14 are: 28, 42, 56, 70, and 84. There are pretty much an infinite number of available multiples.

### Aligned Standard: Grade 4 Operations - 4.OA.4

- Primes and Composite Numbers Step-by-Step Lesson- We go over the difference between primes (can only be divided by themselves and 1) and composites (have more than 2 factors).
- Guided Lesson - A real mix of skills here. Circle all the multiples of 12, list factors from least to greatest, and divisibility.
- Guided Lesson Explanation - Not to toot my own horn, but this explanation makes a great deal of sense.
- Practice Worksheet - A cool little activity I came up with. Color the primes green and the composites yellow.
- Missing Digit Multiplication 5-Pack - What is the missing digit to complete these products.
- Factors 5-Pack - Find the factors of numbers.
- Prime or Composite Numbers Five Worksheet Pack - Identify the integers as prime or composite.
- Matching Worksheet - Match the number and their second multiple. This is a good quick review.

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

### Homework Sheets

We mix up the skills here. You will first look for multiples of a particular number, then write all of the factors of a number. We finish off the homework with a little divisibility practice.

- Multiples Homework - Circle all of the numbers that are a multiple of 9.
- Factors Homework - Write the factors of 20 from smallest to the largest.
- Divisibility Homework - Is the number 45411 divisible by 7?

### Practice Worksheets

This really works on your understanding of multiples, divisibility, and factors. We really clear it up for you.

- Practice 1 - Find the final value of the following problem.
- Practice 2 - A mixed bag of question types.
- Practice 3 - Lots of circles here.

### Math Skill Quizzes

The quizzes are also more mixed then other sections. You start by listing factors. We move on to determining if a number is prime or composite. We finish off with Odds or Evens.

- Factors Quiz - Find all the factors of each number.
- Primes Quiz - Name the numbers as Prime or Composite and list their factors.
- Odds or Evens Quiz - Find all the factors of and label each number as odd or even.

### What Are Factor Pairs?

To understand factor pairs, we have to go back to revisiting the concept of natural numbers. You see, every natural number is a product of at least a one-factor pair. For example, 19 has a single factor pair, which is 1 and 19, because 19 is present in the tables of 1 and 19 itself. The number 32 has many factor pairs, such as 1 and 32, 2 and 16, and 4 and 8. So, by definition, a factor pair are those two natural numbers that are multiplied to get a specific answer.

Notice that 19 has a single factor pair. It is because 19 is a prime number, so it can be said that every prime number has a single factor pair. Let’s take another example by finding out the factor pair of 23. Can you think of any number of tables which answer 23? No? That’s right, 23 does not have another factor pair, because it is a prime number. A few other examples of factor pairs are given below.

- 18 -> (1, 18), (2, 9), (3, 6).

- 24 -> (1, 24), (4, 6), (8, 3)

- 50 -> (1, 50), (2, 25), (5, 10)

### How to Determine Factor Pairs

Here are a series of steps that you can take to find all the factor pairs of a number

**Step 1** - The number 1 and the number itself are the largest pair.

**Step 2** - If the number is even, it is divisible by 2. We continue this on for all the divisibility rules: 3, 4, 5… If a number is divisible by 2, it is also divisible by 4. The same holds true for 3 and 6.

**Step 3** - Walk you way all the way up the number itself.

Put this into action and find all the factor pairs of 24.

**Step 1** - 1 and 24

**Step 2** - It is even, so 2 and 12. We will go up. 3 and 8, 4 and 6. 5 is not a factor, so we reach all those that were present.

**Final answer for 24** - 1 and 24, 2 and 12, 3 and 8, 4 and 6.