Number Factors

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Table Of Contents

What Is A Factor?

Examples of Number Factors

Practice Problems

Answers


What Is A Factor?

A factor is a positive whole number which (exactly) divides into a whole number with a zero remainder. In other words, a whole number divided by a factor gives another whole number exactly. As an example, any even number can be divided by 2 with zero remainder.


Examples of Number Factors

Here are some examples.

The number 6 has factors of 1, 2, 3 and 6 itself. These factors divide into 6 exactly since 6 \div 1 = 6, 6 \div 2 = 3, 6 \div 3 = 2, and 6 \div 6 = 1.

The number 20 has factors of 1, 2, 4, 5, 10 and 20 itself. We can have 1 \times 20 = 20, 2 \times 10 = 20 and 4 \times 5 = 20. Alternatively, we can show that 20 \div 1 = 20, 20 \div 2 = 10, 20 \div 4 = 5, 20 \div 5 = 4, and 20 \div 10 = 2, and 20 \div 20 = 1.

We look at an interesting case. The number 7 has factors of just 1 and 7 itself. Because 7 has two factors which are 1 and itself, the number 7 is an example of a prime number. Other prime numbers include 3, 5, 11, 13, 17 and 19.

Factors are not restricted to numbers. We can use variables such as x. As an example, factors of x^2 are 1, x and x^2 itself.


Practice Problems

1) What are the factors of the number 12?

2) What are the factors of the number 49?

3) What are the factors of the number 25?

4) Is 31 a prime number? Why?

5) What are the factors of x^4?

6) What are the factors of 2x^2?

 


Answers

1) 1, 2, 3, 4, 6 and 12

2) 1, 7, 49

3) 1, 5, 25

4) The factors of 31 are 1, and 31 itself. It is a prime number.

5) Factors of x^4 are 1, x, x^2, x^3 and x^4 itself.

6) Factors of 2x^2 include 1, 2, x, x^2 and 2x^2.

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