JUMP TO TOPIC
Factors of 345: Prime Factorization, Methods, and Examples
In this article, we are going to see different factors of number 345 .
Firstly, we see the factors are those numbers when multiplying those factors of number like in this case 3, 5, and 23 are a prime factor of 345 so when we multiply 3x5x23 give back the original number that which we split and that is equal to 345.
Factors of 345
Here are the factors of number 345.
Factors of 345: 1, 3, 5, 15, 23, 69, 115, and 345
Negative Factors of 345
The negative factors of 345 are similar to its positive aspects, just with a negative sign.
Negative Factors of 345: -1, -3, -5, -15, -23, -69, -115, and -345
Prime Factorization of 345
The prime factorization of 345 is the way of expressing its prime factors in the product form.
Prime Factorization: 3 x 5 x 23
In this article, we will learn about the factors of 345 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 345?
The factors of 345 are 1, 3, 5, 15, 23, 69, 115, and 345. These numbers are the factors as they do not leave any remainder when divided by 345.
The factors of 345 are classified as prime numbers and composite numbers. The prime factors of the number 345 can be determined using the prime factorization technique.
How To Find the Factors of 345 ?
You can find the factors of 345 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.
To find the factors of 345, create a list containing the numbers that are exactly divisible by 345 with zero remainders. One important thing to note is that 1 and 345 are the 345 ‘s factors as every natural number has 1 and the number itself as its factor.
1 is also called the universal factor of every number. The factors of 345 are determined as follows:
\[\dfrac{345}{1} = 345\]
\[\dfrac{345}{3} = 115\]
\[\dfrac{345}{5} = 69\]
\[\dfrac{345}{15} = 23\]
\[\dfrac{345}{23} = 15\]
\[\dfrac{345}{69} = 5\]
\[\dfrac{345}{115} = 3\]
\[\dfrac{345}{345} = 1\]
Therefore, 1, 3, 5, 15, 23, 69, 115, and 345 are the factors of 345.
Total Number of Factors of 345
For 345, there are eight positive factors and eight negative ones. So in total, there are sixteen factors of 345.
To find the total number of factors of the given number, follow the procedure mentioned below:
- Find the factorization/prime factorization of the given number.
- Demonstrate the prime factorization of the number in the form of exponent form.
- Add 1 to each of the exponents of the prime factor.
- Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.
By following this procedure, the total number of factors of 345 is given as:
Factorization of 345 is 1 x 3 x 5 x 23.
The exponent of 1, 3, 5, and 23 is 1.
Adding 1 to each and multiplying them together results in m.
Therefore, the total number of factors of 345 is 16. Eight is positive, and Eight factors are negative.
Important Notes
Here are some essential points that must be considered while finding the factors of any given number:
- The factor of any given number must be a whole number.
- The factors of the number cannot be in the form of decimals or fractions.
- Factors can be positive as well as negative.
- Negative factors are the additive inverse of the positive factors of a given number.
- The factor of a number cannot be greater than that number.
- Every even number has 2 as its prime factor, the smallest prime factor.
Factors of 345 by Prime Factorization
The number 345 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.
Before finding the factors of 345 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.
To start the prime factorization of 345, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.
Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 345 can be expressed as:
345 = 3 x 5 x23
Factors of 345 in Pairs
The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.
For 345, the factor pairs can be found as:
1 x 345 = 345
3 x 115 = 345
5 x 69 = 345
15 x 23 = 345
The possible factor pairs of 345 are given as (1, 345), (3, 115), (5, 69), and (15, 23).
All these numbers in pairs, when multiplied, give 345 as the product.
The negative factor pairs of 345 are given as:
-1 x -345 = 345
-3 x -115 = 345
-5 x -69 = 345
-15 x -23 = 345
It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -3, -5, -15, -23, -69, -115, and -345 are called negative factors of 345.
The list of all the factors of 345, including positive as well as negative numbers, is given below.
Factor list of 345: 1, -1, 3, -3, 5, -5, 15, -15, 23, -23, 69, -69, 115, -115, 345, and -345.
Factors of 345 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 345 are there?
Solution
The total number of Factors of 345 is 16.
Factors of 345 are 1, 3, 5, 15, 23, 69, 115, and 345.
Example 2
Find the factors of 345 using prime factorization.
Solution
The prime factorization of 345 is given as:
345 $\div$ 3 = 115
115 $\div$ 5 = 23
23 $\div$ 23 = 1
So the prime factorization of 345 can be written as:
3 x 5 x 23 = 345