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Factors of 528: Prime Factorization, Methods, and Examples
The factors of 528 are numbers that, when divided by 528, give zero as the remainder. The provided number’s factors can be positive or negative.
This article is all about finding factors using the division method and prime factorization.
Factors of 528
Here are the factors of number 528.
Factors of 528: 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, and 528
Negative Factors of 528
The negative factors of 528 are similar to their positive aspects, just with a negative sign.
Negative Factors of 528: –1, -2, -3, -4, -6, -8, -11, -12, -16, -22, -24, -33, -44, -48, -66, -88, -132, -176, -264, and -528
Prime Factorization of 528
The prime factorization of 528 is the way of expressing its prime factors in the product form.
Prime Factorization: 2 x 2 x 2 x 2 x 3 x 11
In this article, we will learn about the factors of 528 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 528?
The factors of 526 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, and 528. These numbers are the factors as they do not leave any remainder when divided by 528.
The factors of 528 are classified as prime numbers and composite numbers. The prime factors of the number 528 can be determined using the prime factorization technique.
How To Find the Factors of 528?
You can find the factors of 528 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 528, create a list containing the numbers exactly divisible by 528 with zero remainders. One important thing to note is that 1 and 528 are the 528’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 528 are determined as follows:
\[\dfrac{528}{1} = 528\]
\[\dfrac{528}{2} = 264\]
\[\dfrac{528}{3} = 176\]
\[\dfrac{528}{4} = 132\]
\[\dfrac{528}{6} = 88\]
\[\dfrac{528}{8} = 66\]
\[\dfrac{528}{11} = 48\]
\[\dfrac{528}{12} = 44\]
\[\dfrac{528}{16} = 33\]
\[\dfrac{528}{22} = 24\]
Therefore, 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, and 528 are the factors of X.
Total Number of Factors of 528
For 528, there are twenty positive factors and twenty negative ones. So in total, there are 40 factors of 528.
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 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 528 is given as follows:
Factorization of is 1 x 2$^4$ x 3 x 11.
The exponent of 1, 3, and 11 is 1, whereas the exponent of 2 is 4.
Adding 1 to each and multiplying them together results in m.
Therefore, the total number of factors of 528 is 40. Twenty are positive, and twenty 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 2 as its prime factor, the smallest prime factor.
Factors of 528 by Prime Factorization
The number 528 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 528 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 528, 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 528 can be expressed as:
528 = 2 x 2 x 2 x 2 x 3 x 11
Factors of 528 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 528, the factor pairs can be found as:
1 x 528 = 528
2 x 264 = 528
3 x 176 = 528
4 x 132 = 528
6 x 88 = 528
8 x 66 = 528
11 x 48 = 528
12 x 44 = 528
16 x 33 = 528
22 x 24 = 528
The possible factor pairs of 528 are given as (1, 528), (2, 264), (3, 176), (4, 132),(6,88), (8, 66), (11, 48), (12, 44), (16, 33) and (22, 24 ).
All these numbers in pairs, when multiplied, give 528 as the product.
The negative factor pairs of 528 are given as:
-1 x -528 = 528
-2 x -264 = 528
-3 x -176 = 528
-4 x -132 = 528
-6 x -88 = 528
-8 x -66 = 528
-11 x -48 = 528
-12 x -44 = 528
-16 x -33 = 528
-22 x -24 = 528
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, -3, -4, -6, -8, -11, -12, -16, -22, -24, -33, -44, -48, -66, -88, -132, -176, -264, and -528 are called negative factors of 528.
The list of all the factors of 528, including positive as well as negative numbers, is given below.
Factor list of 528: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 11, -11, 12, -12, 16, -16, 22, -22, 24, -24, 33, -33, 44, -44, 48, -48, 66, -66, 88, -88, 132, -132, 176, -176, 264, -264, 528, and -528
Factors of 528 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 528 are there?
Solution
The total number of Factors of 528 is 40.
Factors of 528 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, and 528.
Example 2
Find the factors of 528 using prime factorization.
Solution
The prime factorization of 528 is given as:
528 $\div$ 2 = 264
264 $\div$ 2 = 132
132 $\div$ 2 = 66
66 $\div$ 2 = 33
33 $\div$ 3 = 11
11 $\div$ 11 = 1
So the prime factorization of 528 can be written as:
2 x 2 x 2 x 2 x 3 x 11 = 528