 # Repeated Prime Factors – Definition, Facts, Examples | How to find the Repeated Prime Factors of a Number?

You can improve your knowledge regarding the concept of finding Prime Factors. A factor is one of two or more numbers that divides a given number without a remainder. Here you will learn about repeated prime factors, how to find repeated prime factors and some example problems on repeated prime factors, and so on.

This page makes it easy for you to understand how to find repeated prime factors as we have compiled the step-by-step solutions for all the questions. Assess your strengths and weaknesses by finding the repeated prime factors as a part of your preparation.

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### Repeated Prime Factors – Definition & Meaning

Repeated Prime Factor means a number can have two or more different repeated factors. Let us consider an example of repeated prime factors is 8 = 2 x 2 x 2. Here 2 is said to be a repeated prime factor.

### How do you find Repeated Prime Factors of a Number?

Follow the simple steps listed below to understand how to find repeated prime factors. They are as such
1. First, We will find the prime factors of a given number.
2. Then, write the all-finding prime factors in one place.
3. Now, Count the same number of finding prime factors. If the factor numbers are two or more same numbers then it is a Repeated Prime Factors.

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### Repeated Prime Factors Examples

Example 1:
Find the Repeated Prime Factors of the following Numbers,
(i) 25 (ii) 15 (iii) 49 (iv) 16 (v) 32

Solution:
Given the values
(i) The value is 25
Now, write the prime factors of 25 i.e. 5 x 5 and 25 x 1.
Therefore, the Repeated Prime Factors of 25 are 5 x 5.
(ii) 15
Now, writing 15 in terms of factorization we get 3 x 5, and 5 x 3
In this factorization, there are no repeated prime factors.
Therefore, 15 has no Repeated Prime Factors.
(iii) 49
We can write 49 in terms of the factors as 7 x 7, and 49 x 1.
So, the Repeated Prime Factors of 49 are 7 x 7.
(iv) 16
Writing 14 in terms of factors is 4 x 4, and 2 x 2 x 2 x 2.
Hence, the Repeated Prime Factors of 16 are 4 and 2.
(v) 32
We can express 32 in terms of prime factors is 8×4, 4×8, and 2 x 2 x 2 x 2 x 2.
Therefore, the Repeated Prime Factors of 32 is 2.

Example 2:
Write the Repeated Prime Factors of 125 and 128.

Solution:
Given the values is 125 and 128.
Now, we can express 125 in terms of prime factors as 5 x 5.
Another value is 128. We can write 128 in terms of the prime factors as 2 x 2 x 2 x 2 x 2 x 2 x 2.
Therefore, the Repeated Prime Factors of 125 is 5, and the repeated prime factors of 128 are 2.

Example 3:
Write the Repeated Prime Factors of 432, 81, 900.

Solution:
As given in the question, the value is 432.
We can express 432 in terms of prime factors as 4 x 4 x 3 x 3 x 3
Now, we can express 81 in terms of prime factors as 3 x 3 x 3 x 3.
Writing 900 in terms of prime factors as 5 x 5 x 6 x 6.
Therefore, the Repeated Prime Factors of 432 are 4 and 3, 81 Repeated Prime Factor is 3, and Repeated Prime Factors of 900 are 5, 6.

Example 4:
Write the product value of the below of given Repeated Prime Factors,
(i) 2 x 2 x 3 x 3 x 3
(ii) 7 x 7 x 5

Solution:
(i) Given the Repeated Prime Factors,
Now, we write product value of 2 x 2 x 3 x 3 x 3 is 108.
(ii) 7 x 7 x 5
We can write the product value of 7 x 7 x 5 is 245.
Hence, the product values are 108, and 245.

Example 5:
Find the Prime Factor of 72 using the Division Method. Write its Repeated Prime Factors.

Solution:
Given the value is 72. We can find the prime factors using the division method.
In this method, first, we have to check each number by dividing the composite number.
To get the prime factors of 72, we have to start by dividing them by prime numbers.
72 ÷ 36 = 2
36 ÷ 18= 2
18 ÷ 9 = 2
9 ÷ 3 = 3
3 ÷ 1 = 3
The Prime factors of 72  is 2 x 2 x 2 x 3 x 3.
Therefore, the Repeated Prime Factors of 72 is 2 and 3.

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