
The factors of
85 are 1, 5, 17, and 85 i.e. F85 = {1, 5, 17, 85}. The
factors of 85 are all the numbers that can divide 85 without leaving a
remainder.
We can check if these
numbers are factors of 85 by dividing 85 by each of them. If the result is a
whole number, then the number is a factor of 85. Let's do this for each of the
numbers listed above:
·
1 is a factor of 85
because 85 divided by 1 is 85.
·
5 is a factor of 85
because 85 divided by 5 is 17.
·
17 is a factor of 85
because 85 divided by 17 is 5.
·
85 is a factor of 85
because 85 divided by 85 is 1.
How to Find Factors of 85?
1 and the number
itself are the factors of every number. So, 1 and 85 are two factors of 85. To
find the other factors of 85, we can start by dividing 85 by the numbers
between 1 and 85. If we divide 85 by 2, we get a remainder of 1. Therefore, 2
is not a factor of 85. If we divide 85 by 3, we get a remainder of 1.
Therefore, 3 is not a factor of 85.
Next, we can check if
4 is a factor of 85. If we divide 85 by 4, we get a remainder of 1. Therefore,
4 is also not a factor of 85. If we divide 85 by 5, we get a remainder of 0.
Therefore, 5 is a factor of 85. We can continue this process for all the
possible factors of 85.
Through this process,
we can find that the factors of 85 are 1, 5, 17, and 85. These are the only
numbers that can divide 85 without leaving a remainder.
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Properties of the Factors of 85
The factors of 85 have
some interesting properties. One of the properties is that the sum of the
factors of 85 is equal to 108. We can see this by adding all the factors of 85
together:
1 + 5 + 17 + 85 = 108
Another property of
the factors of 85 is that they are all odd numbers. This is because 85 is an
odd number, and any even number cannot divide an odd number without leaving a
remainder.
Another property of
the factors of 85 is that the prime factors of 85 are 5 and 17.
Applications of the Factors of 85
The factors of 85 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
85 and 34, we need to find the factors of both numbers and identify the largest
factor they have in common. The factors of 85 are 1, 5, 17, and 85. The factors
of 34 are 1, 2, 17, and 34. The largest factor that they have in common is 17.
Therefore, the HCF of 85 and 34 is 17.
Another application of
the factors of 85 is in prime factorization. Prime factorization is the process
of expressing a number as the product of its prime factors. The prime factors
of 85 are 5 and 17. We can express 85 as:
85 = 5 × 17
We can do prime
factorization by division and factor tree method also. Here is the prime
factorization of 85 by division method,

Here is the prime
factorization of 85 by the factor tree method,

Conclusion
The factors of
85 are the numbers that can divide 85 without leaving a remainder. The
factors of 85 are 1, 5, 17, and 85. The factors of 85 have some interesting
properties, such as being odd numbers and having a sum of 108. The factors of 85
have several applications in mathematics, such as finding the highest common
factor and prime factorization.
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