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Factors of 603: Prime Factorization, Methods, and Examples
The numbers that 603 can be divided in all possible ways, leaving zero as the remainder, are the numbers that make up its components.
Given that the given number is obtained by multiplying integers with two factors, its factors may be both positive and negative.
Factors of 603
Here are the factors of number 603.
Factors of 603: 1, 3, 9, 67, 201 and 603
Negative Factors of 603
The negative factors of 603 are similar to its positive aspects, just with a negative sign.
Negative Factors of 603:-1, -3, -9, -67, -201 and -603
Prime Factorization of 603
The prime factorization of 603 is the way of expressing its prime factors in the product form.
Prime Factorization:32 x 671
In this article, we will learn about the factors of 603 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 603?
The factors of 603 are 1, 3, 9, 67, 201, and 603. These numbers are the factors as they do not leave any remainder when divided by 603.
The factors of 603 are classified as prime numbers and composite numbers. The prime factors of the number 603 can be determined using the prime factorization technique.
How To Find the Factors of 603?
You can find the factors of 603 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 603, create a list containing the numbers that are exactly divisible by 603 with zero remainders. One important thing to note is that 1 and 603 are the 603’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 603 are determined as follows:
\[\dfrac{603}{1} = 603\]
\[\dfrac{603}{3} = 201\]
\[\dfrac{603}{9} = 67\]
\[\dfrac{603}{67} = 9\]
\[\dfrac{603}{201} = 3\]
\[\dfrac{603}{603} = 1\]
Therefore, 1, 3, 9, 67, 201, and 603 are the factors of 603.
Total Number of Factors of 603
For 603, there are 6 positive factors and 6 negative ones. So in total, there are 12 factors of 603.
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 603 is given as:
Factorization of 603 is 1 x32 x 671.
The exponent of 1 is 1, 3 is 2, and 67 is 1.
Adding 1 to each and multiplying them together results in 12.
Therefore, the total number of factors of 603 is 12. 6 are positive, and 6 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 603 by Prime Factorization
The number 603 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 603 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 603, 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 603 can be expressed as:
603 = 32 x 671
Factors of 603 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 603, the factor pairs can be found as:
1 x 603 = 603
3 x 201 = 603
9 x 67 = 603
The possible factor pairs of 603 are given as (1, 603), (3, 201), and (9, 67).
All these numbers in pairs, when multiplied, give 603 as the product.
The negative factor pairs of 603 are given as:
-1 x -603 = 603
-3 x -201 = 603
-9 x -67 = 603
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, -9, -67, -201 and -603 are called negative factors of 603.
The list of all the factors of 603, including positive as well as negative numbers, is given below.
Factor list of 603: 1,-1, 3,-3, 9,-9, 67,-67, 603, and -603
Factors of 603 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 603 are there?
Solution
The total number of Factors of 603 is 12.
Factors of 603 are 1, 3, 9, 67, 201, and 603.
Example 2
Find the factors of 603 using prime factorization.
Solution
The prime factorization of 603 is given as:
603 $\div$ 3 = 201
201 $\div$ 3 = 67
67 $\div$ 67 = 1
So the prime factorization of 603 can be written as:
32 x 671 = 603