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Factors of 359: Prime Factorization, Methods, and Examples
The factors of 359 are numbers that give zero as the remainder when divided by 359. Thus, the numbers that ultimately divide the given number are its factors. 359 is an odd prime number. This means it has only two factors.
Further details about its factors are given below.
Factors of 359
Here are the factors of number 359.
Factors of 359: 1, 359
Negative Factors of 359
The negative factors of 359 are similar to their positive aspects, just with a negative sign.
Negative Factors of 359: -1 and -359
Prime Factorization of 359
The prime factorization of 359 is the way of expressing its prime factors in the product form.
Prime Factorization: 1, 359
In this article, we will learn about the factors of 359 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 359?
The factors of 359 are 1 and 359. These numbers are the factors as they do not leave any remainder when divided by 359.
The factors of 359 are classified as prime numbers and composite numbers. The prime factors of the number 359 can be determined using the prime factorization technique.
How To Find the Factors of 359?
You can find the factors of 359 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 359, create a list containing the numbers that are exactly divisible by 359with zero remainders. One important thing to note is that 1 and 359 are the 359’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 359 are determined as follows:
\[\dfrac{359}{1} = 359\]
\[\dfrac{359}{359} = 1\]
Therefore, 1, 359 are the factors of 359.
Total Number of Factors of 359
For 359, there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 359.
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 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 359 is given as:
The factorization of 359 is 1 359.
The exponent of 1, 359 is 1.
Adding 1 to each and multiplying them together results in 4.
Therefore, the total number of factors of 359 is 4. 2 are positive, and two 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 number factors 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 two as its prime factor, the smallest prime factor.
Factors of 359 by Prime Factorization
The number 359 is a prime 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 359 using prime factorization, let us see 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 359, divide by its most minor prime factor. First, determine that the given number is either even or odd. Two will be the smallest prime factor if it is an even number.
Continue splitting the quotient obtained until one is received as the quotient. The prime factorization of 359 can be expressed as:
359 = 1 x 359
Factors of 359 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 359, the factor pairs can be found as:
1 x 359 = 359
The possible factor pairs of 359 are given as (1, 359).
All these numbers in pairs, when multiplied, give 359 as the product.
The negative factor pairs of 359 are given as:
-1 x -359 = 359
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 and -359 are called negative factors of 359.
The list of all the factors of 359, including positive and negative numbers, is given below.
Factor list of 359: 1, -1, 359 and -359
Factors of 359 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 359 are there?
Solution
The total number of Factors of 359 is 4.
Factors of 359 are 1 and 359.
Example 2
Find the factors of 359 using prime factorization.
Solution
The prime factorization of 359 is given as:
359 $\div$ 1 = 359
359 $\div$ 359 = 1
So the prime factorization of 359 can be written as:
1 x 359 = 359