![MCQs [2024]](https://engineeringinterviewquestions.com/wp-content/uploads/2021/02/Interview-Questions-2.png)
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 a 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.
The Factor of 32
A positive integer that is greater than 1 and has only 2 factors is known as prime whereas when a positive integer has more than two factors, they are termed 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.
Find the 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
How Many Factors of 32 are There?
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
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.
Prime Factorization
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 that is multiplied by 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.
Factor Tree of 32
It is a tree of factors and subfactors 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.
Solved Examples
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
Ans: 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:
Some Numerical Questions related to Factors of 32
Here are some questions that can help you get an idea of how to solve questions related to factors of 32 efficiently.
1. How can I distribute 32 toffees among 4 students in a class?
Ans: since the number of toffees available is 32 and the total number of students among whom toffees have to be distributed is 4, therefore, the number of toffees each student will get will be equal to 32/4 which is equal to 8. Thus, each student will get 8 toffees.
2. How many apples are there in 2 boxes if each box is known to contain 16 apples?
Ans: since, it is given in the question that each box contains 16 apples and there are a total of 2 boxes, therefore, the total number of apples present will be 16 X 2, that is 32. Thus, there are 32 apples present.
3. What will be the common factors of 32 and 64?
Ans: as discussed earlier, the factors of 32 are 1, 2, 4, 8, 16, and 32 and the factors of 64 are 1, 2, 4, 8, 16, 32, and 64. Therefore, we can see that all the factors of 32 and 64 are common except for 64. Therefore, 32 and 64 have six factors in common.
4. if you bake 32 cookies that have to be distributed in 8 plates, then how will you do that?
Ans: This question is very similar to the one discussed above. If there are 32 cookies in all and we need to distribute them equally in 8 plates, then 32/8 will be equal to 4. Therefore, 4 cookies will be kept on each of the 8 plates.
5. What will be the product of all the factors of 32?
Ans: 32 contains only one prime factor, that is, 2, therefore, the product of the prime factors of 32 will be 2.
6. if I have 32 blocks, then in how many ways can I make a Rectangle?
Ans: in such questions, evaluating the pair factors helps in analyzing the different ways in which a particular thing can be done. The pair factors of 32 that are possible in this case are (1, 32), (32, 1), (4, 8), and (8, 4). Therefore, you can arrange the 32 blocks in 4 different ways to form a rectangle.