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Factors of 249: Prime Factorization, Methods, and Examples
The factors of 249 are numbers that give off zero as a remainder when 249 is divided from these numbers.
The given number’s factors can be positive and negative, provided that the given number is achieved upon multiplication of two-factor integers.
Factors of 249
Here are the factors of number 249.
Factors of 249: 1, 3, 83 and 249
Negative Factors of 249
The negative factors of 249 are similar to its positive factors, just with a negative sign.
Negative Factors of 249: -1, -3, -83, and -249
Prime Factorization of 249
The prime factorization of 249 is the way of expressing its prime factors in the product form.
Prime Factorization: 3 x 83
In this article, we will learn about the factors of 249 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 249?
The factors of 249 are 1, 3, 83, and 249. All of these numbers are the factors as they do not leave any remainder when divided by 249.
The factors of 249 are classified as prime numbers and composite numbers. The prime factors of the number 249 can be determined using the prime factorization technique.
How To Find the Factors of 249?
You can find the factors of 249 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 249, create a list containing the numbers that are exactly divisible by 249 with zero remainders. One important thing to note is that 1 and 249 are the 249’s factors as every natural number has one and the number itself as its factor.
One is also called the universal factor of every number. The factors of 249 are determined as follows:
\[\dfrac{249}{1} = 249\]
\[\dfrac{249}{3} = 83\]
\[\dfrac{249}{83} = 3\]
\[\dfrac{249}{249} = 1\]
Therefore, 1, 3, 83, and 249 are the factors of 249.
Total Number of Factors of 249
For 249, there are four positive factors and four negative ones. So in total, there are eight factors of 249.
To find the total number of factors of the given number, follow the procedure mentioned below:
- Find the 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 249 is given as:
Factorization of 249 is 1 x 3 x 83
The exponent of 1, 3, and 83 is 1.
Adding 1 to each and multiplying them together results in 8.
Therefore, the total number of factors of 249 is 8. 4 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 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 249 by Prime Factorization
The number 249 is a composite 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 249 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 249, start dividing by its smallest 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 1 is received as the quotient. The prime factorization of 249 can be expressed as:
249 = 3 x 83
Factors of 249 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.
For 249, the factor pairs can be found as:
1 x 249 = 249
3 x 83 = 249
The possible factor pairs of 249 are given as (1, 249) and (3, 83).
All these numbers in pairs, when multiplied, give 249 as the product.
The negative factor pairs of 249 are given as:
-1 x -249 = 249
-3 x -83 = 249
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, -3, -83, and -249 are called negative factors of 249.
The list of all the factors 249, including positive as well as negative numbers, is given below.
Factor list of 249: 1, -1, 3, -3, 83, -83, 249, and -249
Factors of 249 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 249 are there?
Solution
The total number of Factors of 249 is 4.
Factors of 249 are 1, 3, 83, and 249.
Example 2
Find the factors of 249 using prime factorization.
Solution
The prime factorization of 249 is given as:
249 $\div$ 3 = 83
83 $\div$ 83 = 1
So the prime factorization of 249 can be written as:
3 x 83 = 249