[Maths Class Notes] on Factors of 35 Pdf for Exam

When we talk about factors, these are what could divide a number in such a way that they do not leave out a remainder. So, when we talk about factors of 35, what comes to mind? Well, all the numbers can divide the number 35 in such a way that there is no remaining value left. In this case, those numbers are 1, 5, 7, and 35 themselves. 

As you can see, 1 is the smallest factor in this, which will always be the case in all the natural numbers. And when it comes to the largest factor of a natural number, it will always be the number itself. That, in this case, is 35. 

What are All the Factors of 35?

Since all the factors of 35 are the numbers which you can evenly divide to 35, you simply need to divide 35 by all these numbers up to 35 to see which ones give you an even quotient. When you do that, you will find that the following calculations result in an even quotient.

35 ÷ 1 = 35

35 ÷ 5 = 7

35 ÷ 7 = 5

35 ÷ 35 = 1

Hence, the positive factors of 35 are all the numbers that you use to divide for getting an even number. If you list all the factors of 35, you get:

1, 5, 7, 35.

The factors of 35 also include the negative numbers. Hence, all the positive factors of 35 can be converted to negative numbers by adding a negative sign in front of them. These are all the negative factors of the number 35:

-1, -5, -7, -35.

Pair Factors

Pair factors are numbers that are both factors of the same number and give the said number as a result when multiplied. So, if we talk about the number 35 and its factors, we can say that 5 multiplied by 7 is 35. Both the numbers 5 and 7 are factors of 35 and hence counted in the category of pair factors. There are two types of pair factors, Positive Pair Factors and Negative Pair Factors. 

Basically, the factor pairs of 35 are all the combinations of two factors which when multiplied together equal to the number 35. Given below are all the positive factor pairs of 35.

1 × 35 = 35

5 × 7 = 35

7 × 5 = 35

35 × 1 = 35

Hence, the positive factor pairs of 35 are (1, 35) and (5, 7).

The factors of 35 include negative numbers as well. Multiplying a negative number by another negative number equals a positive number. Hence, you can easily convert the positive factor pairs of 35 by putting a minus sign in front of each factor to get the negative factor pairs of 35.

-1 × -35 = 35

-5 × -7 = 35

-7 × -5 = 35

-35 × -1 = 35

Hence, the negative factor pairs of 35 are (-1, -35) and (-5, -7).

Prime Factorization of 35

When any given number is expressed as a product of its factors you can say that the number has been factored. When the factorization contains the prime number only, it is called a prime factorization of that particular number.

Prime Factors of 35

Following are the steps to find the prime factors of 35:

Step 1: Divide the number 35 with the smallest prime factor, i.e. 2.

35 ÷ 2 = 17.5

The quotient cannot be a decimal number, therefore, 2 is not the prime factor of 35.

Step 2: Now, let us take the next prime numbers, i.e. 3.

35 ÷ 3 = 11.67

Therefore, 3 is not a prime factor of 35

Step 3: Similarly, divide 35 by 5.

35 ÷ 5 = 7

So, 5 is a prime factor of 35.

Step 4: Divide the result 7 by the next prime number, which is 7 itself.

7 ÷ 7 = 1

We received 1 as the output which means we cannot proceed further. This means that the prime factors of 35 are 5 and 7 since both these numbers are prime numbers and also factors of 35.

Common Factors

Common Factors are the numbers that are factors of a given number as well as their own factor. To put it simply, let us take the example of 35. The common factors of this number will just be 5 and 7. Why? Well, because these are the numbers which act as factors to the number 35 as well as themselves, 5 x 1 and 7 x 1 respectively.

35 has a very small number of factors. The common factors of the number 35 will be 5 and 7 only since 5 and 7 are factors of 35 as well as factors of themselves respectively (5×1 and 7×1). Thus, common factors of 35 are 5 and 7.

Now, let us look at the method to find the prime factorization of 35.

There are two methods that you can use for finding the prime factors of 35.

1. Division Method

First, you divide the number 35 by the prime numbers 2, 3, 5, 7 etc. in the same order repeatedly as long as the quotient is divisible by that particular number. 

Hence,  the prime factorization of 35 is 5 x 7.

()

2. Factor Tree Method

In this method, you first need to think about any two factors and then think about two factors of the respective number. This goes on until the factors are prime.

You may have different factor trees depending on the starting point, however, all of them would show the same prime factors.

()

Prime Factors

These are the ones which can only be divided by 1 or themselves and the product of which is the given number.