# How to factor

The definition reads that factors are numbers that may be divided into other numbers with no remainder left.

Is the number 6 a factor of the number 6? Well, yes, it is. Is the number 6 a factor of 12? of 18? of 24? Yes, it is.

Now, is the number 6 a factor of the number 13 as well? No, it is not. If you divide 13 by 6, you’ll get 2 with 1 as a remainder. But what now? What are actually the factors involved in the number 13?

1 x 13 equals 13
13 x 1 equals 13
Okay, that’s it.

And since the number 13 can be divided only evenly by 1 and itself, 13, this number is what we call a prime number.

So for prime numbers counts that they can be divided evenly only by 1 and themselves.

Other numbers, for example, 6, 12, or 21, are what we call composite numbers because they can have several (more than 2) factors.

There are many prime numbers. All across the world, mathematicians still have contests to discover the biggest or largest ones.

Examples of Prime Number are 2; 3; 5; 7; 11; 13; 17; 23 …

Mind You: the number ‘One’ (1) is NOT among what we consider prime numbers. The number 1 is very special. It’s a number all on its own.

So now, we’ve looked at prime numbers and factors. In your lessons and classes, you’ll have to find the prime factors in your questions. Finding those numbers is like the most complex breakdown of the factors to get prime numbers. Let’s take a look at a few examples:

The Factors of the number 4 are:

1, 2, 4 (1 x 4, 2 x 2).
The Prime Factors of the number 4 are:

2, 2 (because 1 is not one of the prime numbers, we needed to forget about the 1 x 4).

The Factors of the number 12 are: 1; 2; 3; 4; 6; 12
The Prime Factors of the number 12 are: 2; 2; 3
The Prime Factorization of the number 12 is: 2 x 2 x 3 equals 12

### Video Summary and Quiz

1. List all positive divisors of the given number, in order, from smallest to largest.

$$42$$
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B.
C.
D.

Question 1 of 3

2. List all positive divisors of the given number, in order, from smallest to largest.

$$51$$
A.
B.
C.
D.

Question 2 of 3

3. State the greatest common divisor of the given numbers.

$$32\; and\; 36$$
A.
B.
C.
D.

Question 3 of 3

Next Lesson: Fractions, Decimals, and Percentages

Last Updated on April 12, 2021.