Introduction
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 (5x1 and 7x1). 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.
(Image will be uploaded soon)
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.
(Image will be uploaded soon)
Prime Factors
These are the ones which can only be divided by 1 or themselves and the product of which is the given number.
FAQs on Factors of 35
1. What is prime factorization of 35?
Prime factorization is basically the result of factoring or sectioning any given number into a set of equal components. It has to be done in such a way that every member is a prime number.
One can show this by writing the number itself as the product of two factors. In the instance of 35, those would be the numbers 5 and 7, resulting in 5 x 7. The way it is calculated is by dividing the number 35 starting from the smallest prime number, that is, 2.
2. What is the greatest common factor of 35 and another number?
The greatest common factor or GSF is found pertaining to two numbers. In this, there is a comparison to be done using the method of prime factorization. What really happens is that first, the many prime factors are taken out for the 2 given numbers. After this, the highest common prime factor is determined as the greatest common factor. In case, there is no other such factor for a couple of numbers, it must be said that 1 is their greatest common factor.
Hence, you can say that the greatest common factor of the number 35 or any different number can be determined by comparing their many prime factors.
3. What is the division method to find out factors of 35?
The Division Method is one of the most popular to be used in Math. According to this method, one can go on dividing the number 35 with prime numbers starting from 2, and then, 3, then 5, and so on. This can go on and on until there is a quotient that is fully divisible by the number 35. This way, one also has to ensure that they take out the prime number that leaves out no remainder dividing it by the number 35.
4. How can you use the factor tree method for a number?
When it comes to the Factor Tree Method for any number, what one has to do is simple. They first have to brainstorm any 2 factors of a particular number. This is then followed by taking out 2 and 2 factors of those numbers. This method can go on until the answer comes as a prime number. There might even be instances that a number creates a lot of factor trees. However, when it comes to the end result, you will find that the prime numbers are the same.
5. Are there only positive factors of a number?
No, there are not just positive factors of a number. When it comes to identifying the factors of a number like 35, one can assure that there are both positive and negative types. If we look at all the factors, they are 1, 5, 7, and 35. Now, when it comes to negative factors, they are -1, -5, -7, and -35. As you can see, the latter are just like the former with the negative sign on their front. Click here for all the details.
Furthermore, you can avail all the well-researched and good quality chapters, sample papers, syllabus on various topics from the website of Vedantu and its mobile application available on the play store.