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How do I find the prime factors of 54 using the Division Method?
in Mathematics by Gold Status (31,759 points) | 34 views

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The factors of 54 are the numbers, that can divide 54 completely or evenly. When a pair of factors are multiplied together to produce the 54 , then they are said to be pair factors. The factors divide the number completely. Hence, these factors cannot be a fraction.
Factors of \(54: 1,2,3,6,9,18,27\) and 54

Factor pairs of the number 54 are the whole numbers which are not a fraction or decimal number. To find the factors of a number, 54 , we will use the factorization method.

Some important properties of factors are:
- A factor of any given number is its exact divisor
- For every number, 1 is a factor.
- The factor should be always less than or equal to the number itself
- The number itself is considered as the greatest factor of a number.

 

What are the Factors of \(54 ?\)
The factors of a number are the natural numbers that can divide the original number completely.
Factors of 54
\(1,2,3,6,9,18,27\), and 54
How to Calculate Factors of \(54 ?\)
To find factors of 54 , we have to divide 54 by all natural numbers from 1 to 54 .
- \(54 \div 1=54\)
- \(54 \div 2=27\)
- \(54 \div 3=18\)
- \(54 \div 6=9\)

 

Prime Factors of 54 By Division Method
The number 54 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 54 .
- The first step is to divide the number 54 with the smallest prime factor, say 2 . \(54 \div 2=27\)
- Again, when you divide 54 by 3 , you will get a fractional number and it cannot be a factor and continue with the next prime factor, say 3
\[
\begin{aligned}
&27 \div 3=9 \\
&9 \div 3=3 \\
&3 \div 3=1
\end{aligned}
\]
- Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 54 are written as \(2 \times 3 \times 3 \times 3\) or \(2 \times 3^{3}\), where 2 and 3 are the prime numbers.
by Gold Status (31,759 points)

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