The **factors of
74** are 1, 2, 37, and 74 i.e. F_{74} = {1, 2, 37, 74}. The
factors of 74 are all the numbers that can divide 74 without leaving a
remainder.

We can check if these
numbers are factors of 74 by dividing 74 by each of them. If the result is a
whole number, then the number is a factor of 74. Let's do this for each of the
numbers listed above:

·
1 is a factor of 74
because 74 divided by 1 is 74.

·
2 is a factor of 74
because 74 divided by 2 is 37.

·
37 is a factor of 74
because 74 divided by 37 is 2.

·
74 is a factor of 74
because 74 divided by 74 is 1.

**How to Find Factors of
74?**

1 and the number
itself are the factors of every number. So, 1 and 74 are two factors of 74. To
find the other factors of 74, we can start by dividing 74 by the numbers
between 1 and 74. If we divide 74 by 2, we get a remainder of 0. Therefore, 2
is a factor of 74. If we divide 74 by 3, we get a remainder of 2. Therefore, 3
is not a factor of 74.

Next, we can check if
4 is a factor of 74. If we divide 74 by 4, we get a remainder of 2. Therefore,
4 is not a factor of 74. We can continue this process for all the possible
factors of 74.

Through this process,
we can find that the factors of 74 are 1, 2, 37, and 74. These are the only
numbers that can divide 74 without leaving a remainder.

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**Properties of the
Factors of 74**

The factors of 74 have
some interesting properties. One of the properties is that the sum of the
factors of 74 is equal to 114. We can see this by adding all the factors of 74
together:

1 + 2 + 37 + 74 = 114

Another property of
the factors of 74 is that the prime factors of 74 are 2 and 37 only.

**Applications of the
Factors of 74**

The factors of 74 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
74 and 37, we need to find the factors of both numbers and identify the largest
factor they have in common. The factors of 74 are 1, 2, 37, and 74. The factors
of 37 are 1 and 37. The largest factor that they have in common is 37.
Therefore, the HCF of 74 and 37 is 37.

Another application of
the factors of 74 is in prime factorization. Prime factorization is the process
of expressing a number as the product of its prime factors. The prime factors
of 74 are 2 and 37, since these are the only prime numbers that can divide 74
without leaving a remainder. Therefore, we can express 74 as:

74 = 2 × 37

We can do prime
factorization by division and factor tree method also. Here is the prime
factorization of 74 by division method,

Here is the prime
factorization of 74 by the factor tree method,

**Conclusion**

The **factors of
74** are the numbers that can divide 74 without leaving a remainder. The
factors of 74 are 1, 2, 37, and 74. The factors of 74 have some interesting
properties, such as having a sum of 114. The factors of 74 have several
applications in mathematics, such as finding the highest common factor and
prime factorization.

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