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Factors of 175
Factors of 175 are the numbers which when multiplied in pairs give the product as 175. These factors can be negative as well. The number 175 is an even composite number, which means that it has several factors. In this lesson, we will calculate the factors of 175, the prime factors of 175, and the factors of 175 in pairs. We will also solve some problems to understand this topic better.
Factors of 175: 1, 5, 7, 25, 35, and 175
Prime Factorization of 175: 175 = 5 x 5^{ }× 7
1.  What Are the Factors of 175? 
2.  How to Calculate the Factors of 175? 
3.  Factors of 175 by Prime Factorization 
4.  Factors of 175 in Pairs 
5.  FAQs on Factors of 175 
What Are the Factors of 175?
The factor of a number is that number that divides it completely without leaving any remainder. In order to find the factors of the number 175, we need to divide 175 completely by those numbers which leave no remainder. After dividing 175 by these numbers, we can see that the factors of 175 are 1, 5, 7, 25, 35, and 175.
How to Calculate the Factors of 175?
To calculate the factors of 175, we need to find all the numbers that divide 175, without leaving any remainder.
We start with 1, and then check the following numbers 2, 3, 4, 5, 6, 7, and so on, up to 88 ( approximate half of 175).
We should note that 1 and the number itself will always be a factor of the given number.
Observe the following table to check the factors of 175 by division:
Division  Factor 

175 ÷ 1 
Remainder = 0 Factor = 1 
175 ÷ 5 
Remainder = 0 Factor = 5 
175 ÷ 7 
Remainder = 0 Factor = 7 
175 ÷ 25 
Remainder = 0 Factor = 25 
175 ÷ 35 
Remainder = 0 Factor = 35 
175 ÷ 175 
Remainder = 0 Factor = 175 
Explore factors using illustrations and interactive examples.
 Factors of 17  The factors of 17 are 1 and 17.
 Factors of 125  The factors of 125 are 1, 5, 25, and 125.
 Factors of 250  The factors of 250 are 1, 2, 5, 10, 25, 50, 125, and 250.
 Factors of 110  The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110
 Factors of 112  The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
Important Notes
 While finding factors of any number, we consider only whole numbers and integers.
 Decimal numbers and fractions are not considered as factors of a number.
 All even number have 2 as its factor.
Factors of 175 by Prime Factorization
Prime Factorization of a number refers to breaking down a number into its prime factors. There are different methods that can be used to find the factors of a number using prime factorization.
Division Method
To find the prime factors of 175 using the division method, we will need to follow these steps.
Step 1 Start dividing 175 by the smallest prime number, which can divide it completely. Continue the division with 3, 5, and so on to find the smallest prime factor of the number.
Step 2 After finding the smallest prime factor, which is 5, in this case, obtain the quotient.
175 ÷ 5 = 35
Step 3 Repeat step 1 with the obtained quotient, that is, 35.
Again, the prime factor for 35 would be 5,
35 ÷ 5 = 7
Similarly, 7 ÷ 7 = 1
Thus, the prime factorization of 175 is 5 × 5 × 7.
The Factor Tree Method
We can do the same using the factor tree method.
Hence, the prime factorization of 175 is 5 × 5 × 7.
Thus, all the factors can be written as 1, 5, 7, 25, 35, and 175.
Factors of 175 in Pairs
Pair factors are the factors of a number given in pairs which, when multiplied together, result in that original number.
So, the pair factors of 175 would be any two numbers that would give the product as 175.
The following table represents the different factors of 175 in pairs:
Factor Pair  Pair Factorization 

1 and 175  1 × 175 = 175 
5 and 35  5 × 35 = 175 
7 and 25  7 × 25 = 175 
Negative factor pairs: Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in the above pair factors will also give 175.
The negative factor pairs of 175 would be ( 1, 175 ), ( 5, 35) and ( 7, 25).
Tips and Tricks
 For prime factorization, start dividing the composite numbers until the quotient is a prime number.
 Every number has a minimum of 2 factors, i.e., 1 and the number itself.
 Using the divisibility tests, we can find the factors easily.
 Once you have the prime factorization for the composite numbers, you can express them in exponential form.
Factors of 175 Solved Examples

Example 1 Can you help Emily find the product of all the factors of 175?
Solution
We know, the factors of 175 = 1, 5, 7, 25, 35, 175
Thus, the product of all the factors = 1 × 5 × 7 × 25 × 35 × 175 = 5,359,375

Example 2 How many positive factor pairs does 175 have?
Solution
We know, factors of 175 = 1, 5, 7, 25, 35, 175
Factor pairs = (1, 175), (5, 35), (7, 25)
Hence, the total number of positive factor pairs of 175 = 3
FAQs on factors of 175
1. What are the factors of 175?
The factors of 175 are 1, 5, 7, 25, 35, and 175.
2. Is 175 a perfect square?
We know, 175 = 5 × 5 × 7
Using prime factorization, we see that the square root of 175 cannot be calculated. Thus, 175 is not a perfect square.
3. What are the factors of 175 and 174?
The factor of a number is that number that divides it completely without leaving any remainder.
The factors of 175 = 1, 5, 7, 25, 35, 175
The factors of 174 = 1, 2, 3, 6, 29, 58, 87, 174
4. What is the prime factorization of 175?
Prime Factorization of a number refers to breaking down a number into the form of the product of its prime factors.
So, the prime factorization of 175 is 5 x 5 x 7.
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