Factor of 20 Using Prime Factorization
Introduction
When a pair of factors are multiplied together, the outcome is 20. These are known as factors of 20. These are the numbers 1, 2, 4, 5, 10, and 20. Factor pairs of the number, when multiplied together, provide the original number. The factorization method will be used to find the factors of the number 20. In the factorization approach, the numbers 1 and 20 are first considered as factors, then the other pair of factors of 20 are found. In addition, the prime factors of 20 are examined using prime factorization.
Factors of 20
The numbers that divide 20 perfectly without leaving a remainder are known as the factors of 20. In other words, the factors of 20 are the numbers multiplied in pairs, resulting in the number 20. Because 20 is an even composite number, it has other factors besides 1 and 20. As a result, the factors of 20 are 1, 2, 4, 5, 10, and 20.
Factors of 20: 1, 2, 4, 5, 10 and 20.
Prime Factorization of 20 can be found as:
\( 20=2\times 2\times 5 \) or,
\( 20=2^2\times 5 \)
Factor List of the Number 20
Divisibility rules and division facts can be used to determine the factors of 20. Given below is a table where the first eight numbers are verified to check if they are the factors of 20. After ‘8’ the pattern is repeated.
Factor Tree of 20
Factor Pairs of 20
We already know that the factors of 20 can either be positive or negative. For now, we will focus on the positive factor pairs of 20. The factor pairs of 20 are pairs of numbers that when multiplied together equals 20. As a result, the positive factor pairs of 20 are listed below.
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Rapid Recall
Factors and factor pairs of 20.
Solved Factors of 20 Examples
Example 1: Make a list of the common factors of 20 and 21.
Solution:
The factors of 20 are 1, 2, 4, 5, 10 and 20.
The factors of 21 are 1, 3, 7 and 21.
Thus, the common factor of 20 and 21 is 1.
Example 2: Write down the common factors of 20 and 19.
Solution:
Factors of 20 = 1, 2, 4, 5, 10 and 20.
Factors of 19 = 1 and 19.
As 19 is a prime number, the common factor of 20 and 19 is just 1.
Example 3: Andrew was asked to sort 20 students into different teams. How many students and teams can Andrew sort the students into considering that each team should have an equal number of students.
Solution:
The factor pairs of 20 are (1, 20), (2, 10) and (4, 5). The product of each of these numbers gives us 20.
According to the question, we need to find different combinations of teams and students such that each team has the equal number of students. The different combinations of students and the number of teams can be as follows based on the factor pairs.
In all the combinations given above the number of students are equally distributed.
1, 2, 4, 5, 10, and 20 are the factors of 20.
\(2 \times 2 \times 5 \) or \( 2^2 \times 5\) is the prime factorization of 20.
(1, 20), (4, 5), and (2, 10) are the positive factor pairs of 20.
(-1, -20), (-2, -10), and (-4, -5) are the negative factor pairs of 20.
Yes, a factor of 20 equals 5. When 5 divides 20, the remainder is 0, indicating that 5 is a factor of 20.