The Factors of 195- An Introduction
This article is going to answer the question, what is the factor of 195? A factor of a number is a divisor such that when the divisor divides the given number, then the remainder is zero. By using the factorisation method, we can find the positive factors of a number. But the negative value of the factors of a number is also a factor of the given number. We will consider the positive factors as well as the negative factors; negative whole numbers that can be divided by 195. The result of taking the number 195 and dividing it by one of its factors would be another factor of it.
Let's examine how to identify and list each of the 195 elements. These numbers can be written as individual factors or factor pairs and divided into 195 equal parts. We present them both ways. This is a specific number's mathematical decomposition.
How to Find Factors of 195?
We need to find the smallest divisor that divides 195 completely that is leaving 0 as a remainder. The divisor and the quotient both are the factors of 195. The process will goe on until we reach 195.
Step 1: Divide 195 by the smallest prime number
Since 195 is an odd number, thus it is not divisible by 2
Step 2: Divide 195 by 3
1+9+5=15 which is divisible by 3 thus 3 is a factor of 195.
\[195 \div 3 = 65\]
Thus, 3 and 65 both are factors of 195.
Step 3: Divide 195 by an even number
Since 195 is not divisible by 2, thus it is not divisible by any even number like 4,6,8,10,..194.
Step 4: Divide 195 by 5
Since the digit at unit place is 5, so it is divisible by 5. Thus 5 is a factor of 195
$195 \div 5 = 39$
Thus 5 and 39 both are factors of 195.
Step 5: Divide 195 by 7
After dividing 195 by 7, we get a remainder 3. Thus 7 is not a factor of 195.
Step 6: In the same manner 195 is not divisible by 9 and 11.
Step 7: Divide 195 by 13
$195 \div 13 = 15$
Thus 13 and 15 both are factors of 195.
There factor of 195 are 1, 3, 5, 13, 15, 39, 69, 195.
Negative Factor Pairs
A number is divisible by the negative value of positive factors completely and gives a negative quotient. Thus, the negative value of positive factors are also a factor of a number. The negative factors of 195 are -1, -3, -5, -13, -15, -39, -69, -195.
What are Factor Pairs?
A factor pair consists of any two factors that, when multiplied together, add up to 195. The number 195 is known as the product in mathematics, and the two numbers that may be multiplied together to equal it are known as the factors.
We must first obtain all of the factors of 195 in order to calculate the factors of 195 in pairs. Once you've compiled a list of all of those elements, you can pair them up to produce a list of all possible combinations of factors.
195, 65, 39, 15, 13, 5, 3, and 1 are all of the factors for 195, along with all of their negatives.
List of Factors of 195 in Pairs
The factor pairs of a number look the same as an ordered pair. But factor pairs follow a rule that the product of the elements of the ordered pair is a number whose order pair we are searching for.
The list of the numbers is shown below:
\[1 \times 195 = 195\]
\[3 \times 65 = 195\]
\[5 \times 39 = 195\]
\[13 \times 15 = 195\]
And the negative factor pairs are
\[-1 \times -195 = 195\]
\[-3 \times -65 = 195\]
\[-5 \times -39 = 195\]
\[-13 \times -15 = 195\]
The Prime Factors of 195
First we find a smallest prime number that divides 195 evenly. Then divide the quotient by the smallest prime which divides the quotient evenly. This will go until we get 1 as a quotient. This method is known as prime factorization of 195.
The prime factorization of 195 is $3 \times 5\times 13.$
What is a Factor Tree?
The factor tree of a number is a pictorial representation of the prime factors of the given number. This helps find all the factors of the given number as well as the prime factor of the number.
The factor tree of 195 is shown below:
Factor tree of 195
Number of Factors of 195
The prime factorization of a number helps us find the number of positive factors of the given number. If M is a composite number and \[M = x^ay^bz^c\], then the number of factors of M is (a+1)(b+1)(c+1).
The prime factorization form of 195 is \[195 = 3 \times 5 \times 15\]
The exponent of 3,5,and 13 is 1.
The number of positive factors of 195 is (1+1)(1+1)(1+1) = 8.
Sum of Factors of 195
The factors of 195 are 1,3,5,13,15,39,65,195,-1,-3,-5,-13,-15,-39,-65,-195.
The sum of the positive factors is 1+3+5+13+15+39+65+195 = 336
The sum of the negative factors is -1+(-3)+(-5)+(-13)+(-15)+(-39)+(-65)+(-195) = -336
The Highest Common Factor of 195 and Another Number
The highest common factor of 195 and any other is calculated by listing the factors of both numbers and then selecting the highest common factor of the two, or by simply multiplying all the common prime factors of the two numbers.
Interesting Facts
1 is the only number which is neither prime nor composite.
2 is the smallest prime number.
All prime numbers are odd numbers, except 2.
Solved Examples
Example 1: What is the sum of all the prime factors of 195?
Sol: The prime factors of 195 are 3, 5 and 13. So, the sum of all the prime factors of 195 is 3 + 5 + 13 = 21.
Example 2: Find the highest prime common factor of 195 and 147.
Sol:
The prime factors of 195 are 3,5,13.
195 has the following factors: 1, 3, 5, 13, 15, 39, 65, and 195
The prime factors of 147 are 3,7.
147 has the following factors: 1, 3, 7, 21, 49, and 147
Therefore, the highest prime common factor of 195 and 147 is 3.
Example 3: Find the sum of all factors of 195.
Sol: The factors of 195 are 1, 3, 5, 13, 15, 39, 65, and 195. The sum of all factors of 195 is 1+3+5+13+15+39+65+195= 336.
Conclusion
195 is a composite number rather than a prime number.
The composite number 195 has the following prime factors:
195 = 3 × 5 × 13The factors 1, 3, 5, 13, 15, 39, 65, and 195 and the negatives -1, -3, -5, -13, -15, -39, -65, -195 all of these can exactly divide 195.
List of Related Articles
Practice on Your Own
Q 1: What is the product of the prime factors of 195?
Ans: 195.
Q 2: What are the common factors in 195 and 87.
Ans: 1 and 3.
FAQs on Factors of 195
1: Why isn't a composite number the prime factor of a number?
Only prime numbers are the prime factors of a number. According to the definition of a prime number: a prime number must be greater than 1 and has factors as 1 and itself.
2: Why is 0 not a factor of any number?
0 is not a factor of any number, because if we divide a number by 0 then it becomes undefined.
3: Why is 1 not a prime factor of any number?
The definition of a prime number is, a number greater than 1, which is divisible by exactly 2 positive numbers, i.e., 1 and the number itself. By this definition, 1 is not a prime number since neither it is greater than 1 nor it is divisible by 2 positive numbers.
