A factor of any given number is an exact divisor of that number. Hence, the factors of 35 are all the numbers that are the exact divisor of 35.
You can find the factors of any number by finding the number that divides the number without leaving any remainder or alternatively, the numbers which can multiply together to equal the target number that is being converted.
The factors of 35 are all the integers, both positive and negative whole numbers which you can evenly divide to 35. When you divide the number 35 by a factor of 35, it would equal to another factor of 35. In this article, we would learn what are the factors of 35, factor pairs of 35 and the prime factorization of 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.
Factor Pairs Of 35
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 factorised. When the factorization contains the prime number only, it is called as prime factorization of that particular number.
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.
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.
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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.
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1. What is the prime factorization of 35?
Prime factorization is the result of factoring any given number into a set of components such that every member is a prime number. This is usually written by showing 35 as a product of its prime factors. For the number 35, this result would be 35 = 5 x 7.
2. What is the greatest common factor of 35 and another number?
The greatest common factor of two numbers can be found by comparing the prime factorization (factorization in some cases) of the two numbers and then taking the highest common prime factor. If there is no common factor present, the GCF is 1. This is also called as the highest common factor and is the part of the common prime factors of two numbers. It is known to be the largest factor (largest number) of the two numbers that share as a prime factor. The least common factor (smallest number in common) of any pair of the given integers is 1.
Hence, the greatest common factor of 35 and any other number can be found by comparing their prime factors.
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