We all had the chapter “Factors and multiples” in our mathematics. So what does it mean when we ask “what are the factors of 32?” First of all, we must know that factor is a number that divides another number leaving no remainder behind. For example, 3 and 6 are the factors of 12 because on dividing 12 by 3 we get an exact 4 with no remainder. In the same way, when we divide 12 by 6, we get an exact 2 with no remainder left.

A positive integer which is greater than 1 and has only 2 factors are known as prime whereas when a positive integer has more than two factors, they are termed as composite numbers. 32 is therefore a composite number as it has more than just 2 factors. And all factors of 32 are positive numbers. Thus, All the negative and positive whole numbers that can divide 32 evenly and without leaving any remainder can be called factors of 32.

All factors of 32 are 1, 2, 4, 8, 16, and 32. Therefore, these are the common factors of 32.

To find all factors of 32, we simply have to divide 32 by all the numbers up to 32 to check which number results in an even quotient. On doing that, the results that we got are as follows:

32 ÷ 1 = 32

32 ÷ 2 = 16

32 ÷ 4 = 8

32 ÷ 8 = 4

32 ÷ 16 = 2

32 ÷ 32 = 1

We have already got our answer to the question “what is the factor of 32?” and now for the question “how many factors of 32 are there?” if we count all factors of 32 we will find that there are 6 positive factors of 32 in all. Apart from the positive factors, if we turn to the negative factors, there are 6 negative factors of 32 just like the positive factors of 32. So in general we can say that there are 6 positive and 6 negative common factors of 32.

Other Integer Numbers like 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, cannot be the factors of 32 as they leaves remainder when they divide 32.

Pair factors of 32 can be described as combinations of two factors that are multiplied together to get 32. Let us see how many pairs can be achieved:

1 × 32 = 32

2 × 16 = 32

4 × 8 = 32

8 × 4 = 32

16 × 2 = 32

32 × 1 = 32

These are all paired factors of 32.

What Are Prime Numbers?

A prime number is always greater than 1 and has two factors: one and itself which means that the number cannot be divided evenly by any other number but one.

Prime numbers are just like the building blocks of numbers where all the numbers can be broken down to prime numbers. There is an infinite number of prime numbers, but they are all less frequent as numbers get larger. These are the reasons that make mathematicians enjoy studying and discovering other prime numbers.

What is the prime factorization of 32? Prime factorization is a result of factoring a number into a set of prime numbers. It is a method of breaking down a number as a product of prime numbers. In order words, it is a method to find out which prime numbers can be multiplied to give the original number. For example, 3 x 3 x 3 = 27. In the example, 3 is a prime number which is multiplied to itself several times to give the original number, therefore, this method is known as prime factorization. The prime factorization of 32 are: 2 x 2 x 2 x 2 x 2 = 32

It is a tree of factors and sub-factors which aims to simplify the method of prime factorization. A factor tree can be designed by finding the factors of a number and then finding the factors of the factor of a number. This process continues several times until we have drawn a bunch of prime factors. Here is an example of a factor tree of 32 for you.

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Example 1) find the factors of the following numbers:

i) 120

ii) 360

iii) 428

iv) 84

v) 12

vi) 70

vii) 66

viii) 240

ix) 34

x)162

Solution 1) i) Factors of 120 are:

ii) Factors of 360 are:

iii) Factor of 428 are:

iv) Factors of 84 are:

v) Factors of 12 are:

vi) Factors of 70 are:

vii) Factors of 66 are:

viii) Factors of 240 are:

ix) Factors of 34 are:

x) Factors of 162 are:

FAQ (Frequently Asked Questions)

1. What are the multiples of 32?

A multiple is a number that can be divided by a number without leaving any remainder behind. The first 20 multiples of 32 are: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320, 352, 384, 416, 448, 480, 512, 544, 576, 608, 640,

2. How can we find the greatest common factor of 8 and 32?

If we divide 8 by 1, 2, 4, and 8 and 32 by 1, 2, 4, 8, 16 and 32, we'll see that the largest common factor of both the numbers are 8. There is another method to find out the largest common factor of 8 and 32 multiplying the common prime factor, we will get 1 x 2 x 2 x 2 = 8, which is the greatest common factor of 8 and 32.