The factors of
58 are 1, 2, 29, and 58 i.e. F58 = {1, 2, 29, 58}. The
factors of 58 are all the numbers that can divide 58 without leaving a
remainder.
We can check if these
numbers are factors of 58 by dividing 58 by each of them. If the result is a
whole number, then the number is a factor of 58. Let's do this for each of the
numbers listed above:
·
1 is a factor of 58
because 58 divided by 1 is 58.
·
2 is a factor of 58
because 58 divided by 2 is 29.
·
29 is a factor of 58
because 58 divided by 29 is 2.
·
58 is a factor of 58
because 58 divided by 58 is 1.
How to Find Factors of 58?
1 and the number
itself are the factors of every number. So, 1 and 58 are two factors of 58. To
find the other factors of 58, we can start by dividing 58 by the numbers
between 1 and 58. If we divide 58 by 2, we get a remainder of 0. Therefore, 2
is a factor of 58. If we divide 58 by 3, we get a remainder of 1. Therefore, 3
is not a factor of 58.
Next, we can check if
4 is a factor of 58. If we divide 58 by 4, we get a remainder of 2. Therefore,
4 is not a factor of 58. We can continue this process for all the possible
factors of 58.
Through this process,
we can find that the factors of 58 are 1, 2, 29, and 58. These are the only
numbers that can divide 58 without leaving a remainder.
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Properties of the Factors of 58
The factors of 58 have
some interesting properties. One of the properties is that the sum of the
factors of 58 is equal to 90. We can see this by adding all the factors of 58
together:
1 + 2 + 29 + 58 = 90
Another property of
the factors of 58 is that the prime factors of 58 are 2 and 29.
Applications of the Factors of 58
The factors of 58 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
58 and 29, we need to find the factors of both numbers and identify the largest
factor they have in common. The factors of 58 are 1, 2, 29, and 58. The factors
of 29 are 1, and 29. The largest factor that they have in common is 29.
Therefore, the HCF of 58 and 29 is 29.
Another application of
the factors of 58 is in prime factorization. Prime factorization is the process
of expressing a number as the product of its prime factors. The prime factors
of 58 are 2 and 29 since these are the only prime numbers that can divide 58
without leaving a remainder. Therefore, we can express 58 as:
58 = 2 × 29
We can do prime
factorization by division and factor tree method also. Here is the prime
factorization of 58 by division method,
Here is the prime
factorization of 58 by the factor tree method,
Conclusion
The factors of 58 are the numbers that can divide 58 without leaving a remainder. The factors of 58 are 1, 2, 29, and 58. The factors of 58 have some interesting properties, such as having a sum of 90. The factors of 58 have several applications in mathematics, such as finding the highest common factor and prime factorization.
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