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Factors of 959: Prime Factorization, Methods, and Examples
In this solution, the factor pairs and factors of number 959 are to be discussed.
There are about four positive factors of number 959 those are 1, 7, 173, and 959, and factor pairs are (1, 959), (7, 173).
Factors of 959
Here are the factors of number 959.
Factors of 959: 1, 7, 137, and 959
Negative Factors of 959
The negative factors of 959 are similar to its positive aspects, just with a negative sign.
Negative Factors of 959: -1, -7, -137, and -959
Prime Factorization of 959
The prime factorization of 959 is the way of expressing its prime factors in the product form.
Prime Factorization: 7 x 137
In this article, we will learn about the factors of 959 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 959?
The factors of 959 are 1, 7, 137, and 959. These numbers are the factors as they do not leave any remainder when divided by 959.
The factors of 959 are classified as prime numbers and composite numbers. The prime factors of the number 959 can be determined using the prime factorization technique.
How To Find the Factors of 959?
You can find the factors of 959 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 959, create a list containing the numbers that are exactly divisible by 959 with zero remainders. One important thing to note is that 1 and 959 are the 959’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 959 are determined as follows:
\[\dfrac{959}{1} = 959\]
\[\dfrac{959}{7} = 137\]
\[\dfrac{959}{137} = 7\]
\[\dfrac{959}{959} = 1\]
Therefore, 1, 7, 137, and 959 are the factors of 959.
Total Number of Factors of 959
For 959, there are four positive factors and four negative ones. So in total, there are eight factors of 959.
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 959 is given as:
Factorization of 959 is 7 x 137.
The exponent of 7 and 137 is 1, 1.
Adding 1 to each and multiplying them together results in four.
Therefore, the total number of factors of 959 is eight. Four are positive, and four 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 959 by Prime Factorization
The number 959 is a composite. 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 959 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 959, 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 959 can be expressed as:
959 = 7 x 137
Factors of 959 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 959, the factor pairs can be found as:
1 x 959 = 959
7 x 137 = 959
The possible factor pairs of 959 are given as (1, 959) and (7, 137 ).
All these numbers in pairs, when multiplied, give 959 as the product.
The negative factor pairs of 959 are given as:
-1 x -959 = 959
-7 x -137 = 959
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, -7, -137, and -959 are called negative factors of 959.
The list of all the factors of 959, including positive as well as negative numbers, is given below.
Factor list of 959: 1, -1, 7, -7, 137, -137, 959, and -959
Factors of 959 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 959 are there?
Solution
The total number of Factors of 959 is four.
Factors of 959 are 1, 7, 137, and 959.
Example 2
Find the factors of 959 using prime factorization.
Solution
The prime factorization of 959 is given as:
959 $\div$ 7 = 137
137 $\div$ 137 = 1
So the prime factorization of 959 can be written as:
7 x 137 = 959