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Factors of 469: Prime Factorization, Methods, and Examples
The factors of 469 are the list of numbers that fully divide 469. The remainder is always zero. There are four factors of 469 in total. The number 469 is an odd composite.
This lesson is all about the factors of number 469.
Factors of 469
Here are the factors of number 469.
Factors of 469: 1, 7, 67, and 469
Negative Factors of 469
The negative factors of 469 are similar to their positive aspects, just with a negative sign.
Negative Factors of 469: –1, -7, -67, and -469
Prime Factorization of 469
The prime factorization of 469 is the way of expressing its prime factors in the product form.
Prime Factorization: 7 x 67
In this article, we will learn about the factors of 469 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 469?
The factors of 469 are 1, 7, 67, and 469. These numbers are the factors as they do not leave any remainder when divided by 469.
The factors of 469 are classified as prime numbers and composite numbers. The prime factors of the number 469 can be determined using the prime factorization technique.
How To Find the Factors of 469?
You can find the factors of 469 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 469, create a list containing the numbers that are exactly divisible by 469 with zero remainders. One important thing to note is that 1 and 469 are the 469’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 469 are determined as follows:
\[\dfrac{469}{1} = 469\]
\[\dfrac{469}{7} = 67\]
Therefore, 1, 7, 67, and 469 are the factors of 469.
Total Number of Factors of 469
For 469, there are four positive factors and four negative ones. So in total, there are eight factors of 469.
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 469 is given as:
Factorization of 469 is 1 x 7 x 67.
The exponent of 1, 7, and 67 is 1.
Adding 1 to each and multiplying them together results in eight.
Therefore, the total number of factors of 469 is 8. 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 469 by Prime Factorization
The number 469 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 469 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 469, 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 469 can be expressed as:
469 = 7 x 67
Factors of 469 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 469, the factor pairs can be found as:
1 x 469 = 469
7 x 67 = 469
The possible factor pairs of 469 are given as (1, 469) and (7, 67).
All these numbers in pairs, when multiplied, give 469 as the product.
The negative factor pairs of 469 are given as:
–1 x -469 = 469
-7 x -67 = 469
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, -67, and -469 are called negative factors of 469.
The list of all the factors of 469, including positive as well as negative numbers, is given below.
Factor list of 469: 1, -1, 7, -7, 67, -67, 469, and -469
Factors of 469 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 469 are there?
Solution
The total number of Factors of 469 is four.
Factors of 469 are 1, 7, 67, and 469.
Example 2
Find the factors of 469 using prime factorization.
Solution
The prime factorization of 469 is given as:
469 $\div$ 7 = 67
67 $\div$ 67 = 1
So the prime factorization of 469 can be written as:
a x b = X