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Factors of 590: Prime Factorization, Methods, and Examples
The natural numbers that make up the number 590’s factors completely split it by producing a whole number quotient. There are other variables for 590, including 1, 2, 5, 10, 29, 58, 145, and 590. It is, therefore, a composite number.
When multiplied, the factors that result in the given number constitute factor pairs.
Factors of 590
Here are the factors of number 590.
Factors of 590:1, 2, 5, 10, 59, 118, 295 and 590
Negative Factors of 590
The negative factors of 590 are similar to its positive aspects, just with a negative sign.
Negative Factors of 590: -1, -2, -5, -10, -59, -118, -295 and -590
Prime Factorization of 590
The prime factorization of 590 is the way of expressing its prime factors in the product form.
Prime Factorization: 21 x 51 x 591
In this article, we will learn about the factors of 590 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 590?
The factors of 590 are 1, 2, 5, 10, 59, 118, 295 and 590. These numbers are the factors as they do not leave any remainder when divided by 590.
The factors of 590 are classified as prime numbers and composite numbers. The prime factors of the number 590 can be determined using the prime factorization technique.
How To Find the Factors of 590?
You can find the factors of 590 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 590, create a list containing the numbers that are exactly divisible by 590 with zero remainders. One important thing to note is that 1 and 590 are the 590’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 590 are determined as follows:
\[\dfrac{590}{1} =590\]
\[\dfrac{590}{2} = 295\]
\[\dfrac{590}{5} = 118\]
\[\dfrac{590}{59} = 59\]
\[\dfrac{590}{590} =10\]
\[\dfrac{590}{118} = 5\]
\[\dfrac{590}{295} = 2\]
\[\dfrac{590}{590} = 1\]
Therefore, 1, 2, 5, 10, 59, 118, 295, and 590 are the factors of 590.
Total Number of Factors of 590
For 590, there are 8 positive factors and 8 negative ones. So in total, there are 16 factors of 590.
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 590 is given as:
Factorization of 590 is 21 x 51 x 591.
The exponent of 2, 5, and 59 is 1.
Adding 1 to each and multiplying them together results in 16.
Therefore, the total number of factors of 590 is 16. 8 are positive, and 8 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 590 by Prime Factorization
The number 590 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 590 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 590, 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 590 can be expressed as:
590 = 21 x 51 x 591
Factors of 590 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 590, the factor pairs can be found as:
1 x 590 = 590
2 x 295 = 590
5 x 118 = 590
10 x 59 = 590
The possible factor pairs of 590 are given as (1, 590), (2, 295), (5, 118), and (10, 59).
All these numbers in pairs, when multiplied, give 590 as the product.
The negative factor pairs of 590 are given as:
-1 x -590 = 590
-2 x -295 = 590
-5 x -118 = 590
-10 x -59 = 590
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, -2, -5, -10, -59, -118, -295 and -590 are called negative factors of 590.
The list of all the factors of 590, including positive as well as negative numbers, is given below.
Factor list of 590: 1,-1, 2,-2,5, -5,10, -10,59, -59,118, -118, 295,-295 ,590, and -590
Factors of 590 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 590 are there?
Solution
The total number of Factors of 590 is 16.
Factors of 590 are 1, 2, 5, 10, 59, 118, 295 and 590.
Example 2
Find the factors of 590 using prime factorization.
Solution
The prime factorization of 590 is given as:
590 $\div$ 2 = 295
295 $\div$ 5 =59
59 $\div$ 59 =1
So the prime factorization of 590 can be written as:
21 x 51 x 591 = 590