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Factors of 59: Prime Factorization, Methods, and Examples
The factors of 59 are the integers that when divided by 59, the remainder is zero. This means that the numbers which are completely divisible by 59 are its factors. 59 is a prime number so it has only two factors.
The factors can be positive as well as negative.
Factors of 59
Here are the factors of number 59.
Factors of 59: 1 and 59
Negative Factors of 59
The negative factors of 59 are similar to its positive factors, just with a negative sign.
Negative Factors of 59: -1 and -59
Prime Factorization of 59
The prime factorization of 59 is its product expressed in the form of its prime factors.
Prime Factorization of 59: 1 x 59
In this article, we will learn about the factors of 59 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 59?
The factors of 59 are 1, and 59. Both of these numbers are the factors as they do not leave any remainder when divided by 59.
The factors of 59 are classified as prime numbers and composite numbers. Since 59 is a prime number therefore it does not have any composite number as its factor. The prime factors of the number 59 can also be determined using the technique of prime factorization.
How To Find the Factors of 59?
You can find the factors of 59 by using the rules of divisibility. The rule of divisibility states that any number when divided by any other natural number then it 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 59, create a list containing the numbers that are exactly divisible by 59 with zero remainders. One important thing to note is that 1 and 59 are the factors of 59 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 59 are determined as follows:
\[\dfrac{59}{1} = 59\]
As 59 is a prime number so it has only two factors. Therefore, 1, and 59 are the factors of 59.
Total Number of Factors of 59
For 59 there are 2 positive factors as found above and 2 negative factors. So in total, there are 4 factors of 59.
To find the total number of factors of the given number, follow the procedure mentioned below:
- Find the 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 59 is given as:
The prime factorization of 59 is 1 x 59.
The exponent of both 1 and 59 is 1.
Adding 1 to each and multiplying them together results in 4.
Therefore, the total number of factors of 59 is 4.
Important Notes
Here are some important 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 which is the smallest prime factor.
Factors of 59 by Prime Factorization
The number 59 is a prime number. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.
Before finding the factors of 59 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 59, start dividing by its smallest 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 59 can be expressed as:
Prime Factorization of 59 = 1 x 59
Factors of 59 in Pairs
The factor pairs are the duplet of numbers that when multiplied together result in the factorized number. Depending upon the total number of factors of the given numbers, factor pairs can be more than one.
For 59, the factor pairs can be found as:
1 x 59 = 59
The possible factor pair of 59 is (1, 59).
Both of these numbers in pairs, when multiplied, give 59 as the product.
The negative factor pairs of 59 are given as:
-1 x -59 = 59
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 -59 are called negative factors of 59.
Factor List
The list of all the factors of 59 including positive as well as negative numbers is given as:
Factor list: 1, -1, 59, and -59
Factors of 59 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 59 are there?
Solution
The total number of Factors of 59 is 4. Two of them are positive and two are negative.
Example 2
Find the factors of 59 using prime factorization.
Solution
The prime factorization of 59 is given as:
59 $\div$ 1 = 59
So the prime factorization of 59 can be written as:
1 x 59 = 59