The **factors of
90** are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90 i.e. F_{90} = {1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90}. The factors of 90 are those numbers that can divide 90 without leaving a remainder.

We can check if these
numbers are factors of 90 by dividing 90 by each of them. If the result is a
whole number, then the number is a factor of 90. Let's do this for each of the
numbers listed above:

·
1 is a factor of 90
because 90 divided by 1 is 90.

·
2 is a factor of 90
because 90 divided by 2 is 45.

·
3 is a factor of 90
because 90 divided by 3 is 30.

·
5 is a factor of 90
because 90 divided by 5 is 18.

·
6 is a factor of 90
because 90 divided by 6 is 15.

·
9 is a factor of 90
because 90 divided by 9 is 10.

·
10 is a factor of 90
because 90 divided by 10 is 9.

·
15 is a factor of 90
because 90 divided by 15 is 6.

·
18 is a factor of 90
because 90 divided by 18 is 5.

·
30 is a factor of 90
because 90 divided by 30 is 3.

·
45 is a factor of 90
because 90 divided by 45 is 2.

·
90 is a factor of 90
because 90 divided by 90 is 1.

**How to Find Factors of
90?**

1 and the number
itself are the factors of every number. So, 1 and 90 are two factors of 90. To
find the other factors of 90, we can start by dividing 90 by the numbers
between 1 and 90. If we divide 90 by 2, we get a remainder of 0. Therefore, 2
is a factor of 90. If we divide 90 by 3, we get a remainder of 0. Therefore, 3
is also a factor of 90.

Next, we can check if
4 is a factor of 90. If we divide 90 by 4, we get a remainder of 2. Therefore,
4 is not a factor of 90. We can continue this process for all the possible
factors of 90.

Through this process,
we can find that the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and
90. These are the only numbers that can divide 90 without leaving a remainder.

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**Properties of the
Factors of 90**

The factors of 90 have
some interesting properties. One of the properties is that the sum of the
factors of 90 is equal to 234. We can see this by adding all the factors of 90
together:

1 + 2 + 3 + 5 + 6 + 9
+ 10 + 15 + 18 + 30 + 45 + 90 = 234

Another property of
the factors of 90 is that they are all composite numbers except 1, 2, 3, and 5.

**Applications of the
Factors of 90**

The factors of 90 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
90 and 120, we need to find the factors of both numbers and identify the
largest factor they have in common. The factors of 90 are 1, 2, 3, 5, 6, 9, 10,
15, 18, 30, 45, and 90. The factors of 120 are 1, 2, 3, 5, 6, 8, 10, 12, 15,
20, 24, 30, 40, 60, and 120. The largest factor that they have in common is 30.
Therefore, the HCF of 90 and 120 is 30.

Another application of
the factors of 90 is in prime factorization. Prime factorization is the process
of expressing a number as the product of its prime factors. The prime factors
of 90 are 2, 3, and 5, since these are the only prime numbers that can divide 90
without leaving a remainder. Therefore, we can express 90 as:

90 = 2 × 3 × 3 × 5

We can do prime
factorization by division and factor tree method also. Here is the prime
factorization of 90 by division method,

∴ 90 = 2 × 3 × 3 ×
5

Here is the prime
factorization of 90 by the factor tree method,

∴ 90 = 2 × 3 × 3 ×
5

**Conclusion**

The **factors of
90** are the numbers that can divide 90 without leaving a remainder. The
factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. The factors of 90
have some interesting properties, such as having a sum of 234. The factors of 90
have several applications in mathematics, such as finding the highest common
factor and prime factorization.

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