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Factors of 998: Prime Factorization, Methods, and Examples
There exist some number on the number line that completely divides 998 i.e. they give a whole number as quotient and zero as the remainder when 998 is divided by them. Such numbers are called the factors of 998.
the article has further detailed information on factors of 998.
Factors of 998
Here are the factors of number 998.
Factors of 998: 1, 2, 499, and 998
Negative Factors of 998
The negative factors of 998 are similar to its positive aspects, just with a negative sign.
Negative Factors of 998: -1, -2, -499, and -998
Prime Factorization of 998
The prime factorization of 998 is the way of expressing its prime factors in the product form.
Prime Factorization: 2 x 499
In this article, we will learn about the factors of 998 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 998?
The factors of 998 are 1, 2, 499, and 998. These numbers are the factors as they do not leave any remainder when divided by 998.
The factors of 998 are classified as prime numbers and composite numbers. The prime factors of the number 998 can be determined using the prime factorization technique.
How To Find the Factors of 998?
You can find the factors of 998 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 998, create a list containing the numbers that are exactly divisible by 998 with zero remainders. One important thing to note is that 1 and X are the 998’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 998 are determined as follows:
\[\dfrac{998}{1} = 998\]
\[\dfrac{998}{2} = 449\]
\[\dfrac{998}{499} = 2\]
\[\dfrac{998}{998} = 1\]
Therefore, 1, 2, 499, and 998 are the factors of 998.
Total Number of Factors of 998
For 998, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 998.
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 998 is given as:
Factorization of 998 is 1 x 2 x 499.
The exponent of 1, 2, and 499 is 1.
Adding 1 to each and multiplying them together results in 998.
Therefore, the total number of factors of 998 is 8. 4 are positive, and 4 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 998 by Prime Factorization
The number 998 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 998 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 998, 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 998 can be expressed as:
998 = 2 x 499
Factors of 998 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 998, the factor pairs can be found as:
1 x 998 = 998
2 x 499 = 998
The possible factor pairs of 998 are given as (1, 998) and (2, 499).
All these numbers in pairs, when multiplied, give 998 as the product.
The negative factor pairs of 998 are given as:
-1 x -998 = 998
-2 x -499 = 998
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, -499, and -998 are called negative factors of 998.
The list of all the factors of 998, including positive as well as negative numbers, is given below.
Factor list of 998: 1, -1, 2, -2, 499, -499, 988, and -998
Factors of 998 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 998 are there?
Solution
The total number of Factors of 998 is 4.
Factors of 998 are 1, 2, 499, and 998.
Example 2
Find the factors of 998 using prime factorization.
Solution
The prime factorization of 998 is given as:
998 $\div$ 2 = 499
499 $\div$ 499 = 1
So the prime factorization of 998 can be written as:
2 x 499 = 998