
The factors of
42 are 1, 2, 3, 6, 7, 14, 21, and 42 i.e. F42 = {1, 2,
3, 6, 7, 14, 21, 42}. The factors of 42 are all the numbers that can divide 42
without leaving a remainder.
We can check if these
numbers are factors of 42 by dividing 42 by each of them. If the result is a
whole number, then the number is a factor of 42. Let's do this for each of the
numbers listed above:
·
1 is a factor of 42
because 42 divided by 1 is 42.
·
2 is a factor of 42
because 42 divided by 2 is 21.
·
3 is a factor of 42
because 42 divided by 3 is 14.
·
6 is a factor of 42
because 42 divided by 6 is 7.
·
7 is a factor of 42
because 42 divided by 7 is 6.
·
14 is a factor of 42
because 42 divided by 14 is 3.
·
21 is a factor of 42
because 42 divided by 21 is 2.
·
42 is a factor of 42
because 42 divided by 42 is 1.
How to Find Factors of 42?
1 and the number
itself are the factors of every number. So, 1 and 42 are two factors of 42. To
find the other factors of 42, we can start by dividing 42 by the numbers
between 1 and 42. If we divide 42 by 2, we get a remainder of 0. Therefore, 2
is a factor of 42. If we divide 42 by 3, we get a remainder of 0. Therefore, 3
is also a factor of 42.
Next, we can check if
4 is a factor of 42. If we divide 42 by 4, we get a remainder of 2. Therefore,
4 is not a factor of 42. We can continue this process for all the possible
factors of 42.
Through this process,
we can find that the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. These are
the only numbers that can divide 42 without leaving a remainder.
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Properties of the Factors of 42
The factors of 42 have
some interesting properties. One of the properties is that the sum of the
factors of 42 is equal to 96. We can see this by adding all the factors of 42
together:
1 + 2 + 3 + 6 + 7 + 14
+ 21 + 42 = 96
Another property of
the factors of 42 is that the prime factors of 42 are 2, 3, and 7.
Applications of the Factors of 42
The factors of 42 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
42 and 30, we need to find the factors of both numbers and identify the largest
factor they have in common. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 42. The largest factor that
they have in common is 6. Therefore, the HCF of 42 and 30 is 6.
Another application of
the factors of 42 is in prime factorization. Prime factorization is the process
of expressing a number as the product of its prime factors. The prime factors
of 42 are 2, 3, and 7, since these are the only prime numbers that can divide 42
without leaving a remainder. Therefore, we can express 42 as:
42 = 2 × 3 × 7
We can do prime
factorization by division and factor tree method also. Here is the prime
factorization of 42 by division method,

Here is the prime
factorization of 42 by the factor tree method,

Conclusion
The factors of
42 are the numbers that can divide 42 without leaving a remainder. The
factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The factors of 42 have some
interesting properties, such as having a sum of 96. The factors of 42 have
several applications in mathematics, such as finding the highest common factor
and prime factorization.
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