
The factors of
169 are 1, 13, and 169 i.e. F169 = {1, 13, 169}. The
factors of 169 are all the numbers that can divide 169 without leaving a
remainder.
We can check if these
numbers are factors of 169 by dividing 169 by each of them. If the result is a
whole number, then the number is a factor of 169. Let's do this for each of the
numbers listed above:
·
1 is a factor of 169
because 169 divided by 1 is 169.
·
13 is a factor of 169
because 169 divided by 13 is 13.
·
169 is a factor of 169
because 169 divided by 169 is 1.
How to Find Factors of 169?
1 and the number
itself are the factors of every number. So, 1 and 169 are two factors of 169.
To find the other factors of 169, we can start by dividing 169 by the numbers
between 1 and 169. If we divide 169 by 2, we get a remainder of 1. Therefore, 2
is not a factor of 169. If we divide 169 by 3, we get a remainder of 1.
Therefore, 3 is not a factor of 169.
Next, we can check if
4 is a factor of 169. If we divide 169 by 4, we get a remainder of 1.
Therefore, 4 is not a factor of 169. We can continue this process for all the
possible factors of 169.
Through this process,
we can find that the factors of 169 are 1, 13, and 169. These are the only
numbers that can divide 169 without leaving a remainder.
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Properties of the Factors of 169
The factors of 169
have some interesting properties. One of the properties is that the sum of the
factors of 169 is equal to 183. We can see this by adding all the factors of 169
together:
1 + 13 + 169 = 183
Another property of the
factors of 169 is that they are all odd numbers. This is because 169 is an odd
number, and any even number cannot divide an odd number without leaving a
remainder.
Another property of
the factors of 169 is that the prime factor of 169 is 13 only.
Applications of the Factors of 169
The factors of 169
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
169 and 26, we need to find the factors of both numbers and identify the
largest factor they have in common. The factors of 169 are 1, 13, and 169. The
factors of 26 are 1, 2, 13, and 26. The largest factor that they have in common
is 13. Therefore, the HCF of 169 and 26 is 13.
Another application of
the factors of 169 is in prime factorization. Prime factorization is the
process of expressing a number as the product of its prime factors. The only
prime factor of 169 is 13. We can express 169 as:
169 = 13 × 13
We can do prime
factorization by division and factor tree method also. Here is the prime
factorization of 169 by division method,

Here is the prime
factorization of 169 by the factor tree method,

Conclusion
The factors of 169 are the numbers that can divide 169 without leaving a remainder. The factors of 169 are 1, 13, and 169. The factors of 169 have some interesting properties, such as being odd numbers and having a sum of 183. The factors of 169 have several applications in mathematics, such as finding the highest common factor and prime factorization.
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