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A factor of a number is any integer that divides evenly into that number without any remainders. Furthermore, the Factors of 21 are important whilst solving mathematical problems. Moreover, in this blog, you will learn about the Factors of 21, their Sum, their Negative factors, Factor pairs and Factors of 21 by the Division Method.
What are the Factors of 21?
The Factors of 21 are all the positive integers that can divide 21 with no remainder. These factors are as follows:
- 1
- 3
- 7
- 21
Here is the logic behind it:
- Dividing 21 by 1 results in 21, with no remainder.
- Dividing 21 by 3 results in 7, with no remainder.
- Dividing 21 by 7 results in 3, with no remainder.
- Dividing 21 by 21 results in 1, with no remainder.
Therefore, 1, 3, 7, and 21 are all Factors of 21. Moreover, it is important to remember that 1 and the number itself (21 in this case) are always considered factors of any number.
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What is the Sum of the Factors of 21?
The sum of the Factors of 21 can be found by adding all the factors together. In this case, the sum would be:
1 + 3 + 7 + 21 = 32
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What are the Factors of Negative 21?
The concept of factors applies to negative numbers as well. The factors of negative 21 are all the integers that divide evenly into -21 with no remainder. Additionally, these factors are identical to the factors of 21, just with the negative signs:
- -1
- -3
- -7
- -21
The reasoning behind this is that multiplying any factor of 21 by -1 will result in a factor of -21.
For example, 3 x -1 = -3, which is a factor of -21.
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What are the Factor Pairs of 8?
A Factor pair of a number is a combination of two factors that multiply to give the original number. Here the Factor Pairs of 21 are:
- (1, 21)
- (3, 7)
Therefore, each factor pair is a way to express 21 as the outcome of two integers.
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Factors of 21 by Division Method
Furthermore, the Division Method is a direct way to find the factors of a particular number. Here is how it works for 21:
- Start with 2, the smallest possible positive factor (excluding 1).
- Then, divide 21 by 2. Since 21 is not divisible by 2 (there is a remainder of 1), hence 2 is not a factor.
- Move on to the next integer which is 3. Divide 21 by 3. We get 7 with no remainder hence 3 is a Factor of 21.
- Next, continue dividing 21 by the factors you have found so far. Since 3 is a factor now try dividing 21 by 7 (another factor of 3). Moreover, dividing 21 by 7 results in 3, with no remainder, thus proving that 7 is a factor.
- Since you have found factors greater than the square root of 21 (which is approximately 4.6), you can stop here. Any other factors would be mirrored by dividing 21 by the factors already discovered (e.g., dividing by 21 would be the same as dividing by 1).
Therefore, using the Division method, you would arrive at the same set of factors for 21 which are 1, 3, 7, and 21.
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