
The factors of
20 are 1, 2, 4, 5, 10, and 20 i.e. F20 = {1, 2, 4, 5,
10, 20}. The factors of 20 are all the numbers that can divide 20 without
leaving a remainder.
We can check if these
numbers are factors of 20 by dividing 20 by each of them. If the result is a
whole number, then the number is a factor of 20. Let's do this for each of the
numbers listed above:
·
1 is a factor of 20
because 20 divided by 1 is 20.
·
2 is a factor of 20
because 20 divided by 2 is 10.
·
4 is a factor of 20
because 20 divided by 4 is 5.
·
5 is a factor of 20
because 20 divided by 5 is 4.
·
10 is a factor of 20
because 20 divided by 10 is 2.
·
20 is a factor of 20
because 20 divided by 20 is 1.
How to Find Factors of 20?
1 and the number
itself are the factors of every number. So, 1 and 20 are two factors of 20. To
find the other factors of 20, we can start by dividing 20 by the numbers
between 1 and 20. If we divide 20 by 2, we get a remainder of 0. Therefore, 2
is a factor of 20. If we divide 20 by 3, we get a remainder of 2. Therefore, 3
is not a factor of 20.
Next, we can check if
4 is a factor of 20. If we divide 20 by 4, we get a remainder of 0. Therefore,
4 is a factor of 20. We can continue this process for all the possible factors
of 20.
Through this process,
we can find that the factors of 20 are 1, 2, 4, 5, 10, and 20. These are the
only numbers that can divide 20 without leaving a remainder.
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Properties of the Factors of 20
The factors of 20 have
some interesting properties. One of the properties is that the sum of the
factors of 20 is equal to 42. We can see this by adding all the factors of 20
together:
1 + 2 + 4 + 5 + 10 + 20
= 42
Another property of
the factors of 20 is that the prime factors of 20 are 2, and 5 only.
Applications of the Factors of 20
The factors of 20 have
several applications in mathematics. One of the applications is in finding the
highest common factor (HCF) of two or more numbers. The HCF is the largest
factor that two or more numbers have in common. For example, to find the HCF of
20 and 24, we need to find the factors of both numbers and identify the largest
factor they have in common. The factors of 20 are 1, 2, 4, 5, 10, and 20. The
factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The largest factor that they
have in common is 4. Therefore, the HCF of 20 and 24 is 4.
Another application of
the factors of 20 is in prime factorization. Prime factorization is the process
of expressing a number as the product of its prime factors. The prime factors
of 20 are 2, and 5 since these are the only prime numbers that can divide 20
without leaving a remainder. Therefore, we can express 20 as:
20 = 2 × 2 × 5
We can do prime
factorization by division and factor tree method also. Here is the prime
factorization of 20 by division method,

Here is the prime
factorization of 20 by the factor tree method,

Conclusion
The factors of 20 are the numbers that can divide 20 without leaving a remainder. The factors of 20 are 1, 2, 4, 5, 10, and 20. The factors of 20 have some interesting properties, such as having a sum of 42. The factors of 20 have several applications in mathematics, such as finding the highest common factor and prime factorization.
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