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Factors of numbers are positive integers that can divide that particular number evenly. When we multiply two numbers to get a product, then the two numbers multiplied are the factors of the third number derived as a product. To find factors of a particular number, we have two ways, one is the multiplication method and the second is the division method. Factors in real life can be used to arrange things in patterns like sweets in a box, distribute chocolates among the children, arrange sitting patterns, etc, so it is important to know about factors and finding factors of a number as it has many real-life applications.
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What Do You Mean by Factors?
Factors are the numbers that exactly divide a number without leaving any remainder other than zero. As the factor of a number exactly divides the number, it is the divisor of the given number. For example, 1,2 and 4 divide the number 4 exactly so, 1,2 and 4 can be called as factors of the number “4”. On the other hand, multiples are the products of the number obtained by multiplying two numbers. The multiples of a number are in a way opposite to the factors as they are infinite and are products rather than being divisors.
Different factors of 20
The factors of 20 are all the positive and negative integers which give you the result as number 20 when you multiply two numbers together. The factor pairs of 20 are the whole numbers that can be either positive or negative but cannot be a fraction or a decimal number. To find all factors of 20, you can use the prime factorization of 20 methods.
In the prime factorization method, you need to first consider the two numbers 1 and 20 as the factors and then continue to find the other pair of multiples of 20 that would give you the results as an original number. For understanding this method in a better way, read the article below for finding the factors of 20 in pairs. Also, you will find the method to find the prime factors of 20 by using the division method.
The factor pairs of 20 are the combinations of two factors which when multiplied together equal to the number 20. Given below are all the positive factor pairs of 20 and all the negative factor pairs of 20.
Factor Pairs of 20
The factors of 20 consists of negative pairs as well because multiplying two negative numbers gives you a positive integer. Hence, you can simply put a minus sign in front of all the numbers of the factor pairs of 20.
How to Find the Factors of 20?
To find all factors of 20, follow the following steps:
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The first step is writing down the number 20.
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Then, find the two numbers such that they give the result as 20 when you multiply them together. For example, 2 and 10. Multiplying them gives you 2 × 10 = 20.
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You would know that 2 is a prime number and has only two factors, that is, 1 and the number itself. Hence, you cannot factorize 2 further since 2 x 1 = 2.
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However, 10 is a composite number and not a prime number. Hence, you can factorize it further as 10 = 2 × 5 × 1.
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Therefore, the factorization of 20 can be written as:
20 = 2 × 2 × 5 × 1
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Finally, you need to write down all the unique numbers that you can obtain from the number 20. Doing so you get,
20 = 2 × 2 × 5 × 1
Hence, all the factors of 20 are 1, 2, 4, 5, 10, and 20.
Prime Factorization of 20
Since the number 20 is a composite number, it consists of prime factors. Now, let us find the prime factors of 20 using the prime factorization method.
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The first step is dividing the number 20 with the smallest prime factor, which is 2 in this case.
Doing so, you get, 20 ÷ 2 = 10
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Now, again, divide the number 10 by 2 since 10 is a composite number and can be further divided.
Diving 10 by 2, you get, 10÷ 2 = 5
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Now, if you divide 5 by 2 you would get a fractional number, and that cannot be a factor.
So, the next step is to proceed with the next prime number which is 5.
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Since 5 is also a prime number and cannot be divided further, you divide it by the number itself.
Dividing the number 5 by itself gives you 5 ÷ 5 = 1
Now, you have received 1 at the end of the division process and it is not possible to proceed further.
Hence, the prime factors of 20 can be written as 2 × 2 × 5, or 22 × 5,
where 2 and 5 are the prime factors of 20.
For prime numbers, there are only two factors i.e, 1 and the number itself and for the composite numbers, there are more than 2 factors apart from 1 and itself. Following are the properties of factors of a number:
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Every number has a common factor for all, which is “1”
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Every natural number has another common factor which is the number itself making all the natural numbers having 1 and themselves as a compulsory factor of it.
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Whole numbers have at least two factors other than 0 and 1 as factors.
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Factors can not be greater than the number as every factor is less than or equal to it.
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Unlike the multiples, the number of factors for a given number is finite.
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Factors of a number can be figured out with the help of the multiplication or division method.
This is how the factors of 20 can be determined. In fact, you can determine the factors of other numbers using the techniques followed by the experts of Vedantu. Find out more about the factors of 20 by logging into the website to develop your concepts accordingly.
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