## Factor of 175 : An Introduction

A factor is a number that completely divides the original number. Real numbers that can evenly divide the original number are factors of $175$. There is no residue if $"x"$ is the factor of $175$, since $"x"$ divides $175$ into equal parts. For instance, $24$ divided by $4$ is $6$, then 4 is the component of $24$. Consequently, $4$ divides $24$ into six equal parts, leaving $0$ as the remainder. Since $175$ can only be divided by $1, 5, 7, 25, 35 and 175$. So these are factors of 175.

Let's use straightforward methods in this article to determine the factors, pair factors, and prime factors of $175$.

## What are the Factors of $175$?

The natural numbers that can divide the number $175$ evenly are factors of $175$. These factors divide the original number into equal numbers of parts. For example, $175$ is divisible by $5$. So, $175$ divided by $5$ is equal to $35$. Hence, $5$ divides the number $175$ into $35$ equal parts.

We can determine the other factors of $175$ with the help of the division method. $175$ has more than two factors. Thus, it is a composite number.

## How to Find Factors of $175$?

The natural numbers that can divide the number $175$ evenly are factors of $175$. So the way you find and list all of the factors of $175$ is to go through every number up to and including $175$ and check which numbers result in an even quotient.

In the division method, the factors of $175$ are found by dividing the number $175$ by different integer numbers. If the integer divides $175$ exactly without leaving a remainder, then the integer is a factor of $175$. Let's start dividing $175$ by $1$ and proceed with the different integers.

$175 \div 1 = 175$

$175 \div 2 = 87.5$ So, 2 is not a factor of 175.

$175 \div 5 = 35$

$175 \div 7 = 25$

$175 \div 25 = 7$

$175 \div 35 = 5$

$175 \div 175 = 1$

Therefore, the factors of $175$ are 1, 5, 7, 25, 35 and 175.

## Prime Factorisation of $175$

Prime factorization is the process of finding the prime terms or prime factors which, when multiplied, give the original number.

Prime Factorization of 175

Take a pair factor of $175$, say $\left ( 1, 175 \right )$

As the number $1$ is neither prime nor composite, it cannot be split further. Take the other factor, $175$, which is a composite number, and it can be factored further into its prime factors.

Thus, $175$ is written as the product of $7$ and $25$. Here, $7$ is a prime number, $25$ is a composite number, and the number $25$ can be written as the product of $5 and $5.

Write the number $175$ as the product of its prime factors.

So, $175$ is written as $5 \times 5 \times 7$.

Therefore, the prime factorization of $175$ is $5 \times 5 \times 7$ or $5^2 \times 7$, where $5$ and $7$ are prime numbers.

Factor Tree

## Pair Factors of $175$

A factor pair is a pair of numbers that, when multiplied, will result in an original number(or the same product).

To calculate the factor of a number, factors are frequently presented as pairs of numbers. They are referred to as factor pairs. For example- factor pairs of $12$ include, $\left ( 1, 12 \right )$ and $\left ( 3, 4 \right )$.

The pair factors of $175$ are expressed in positive and negative forms. Since the number $175$ is composite, it has more than one-factor pair. Thus, the positive and negative pair factors of $175$ are given below:

Positive Pair Factor of $175$:

$1 \times 175 = 175$

$5 \times 35 = 175$

$7 \times 25 = 175$

Therefore, the positive pair factors of $175$ are $\left ( 1, 175 \right )$, $\left ( 5, 35 \right )$ and $\left ( 7, 25 \right )$.

Negative Pair Factor of $175$:

$-1 \times -175 = 175$

$-5 \times -35 = 175$

$-7 \times -25 = 175$

Therefore, the negative pair factors of $175$ are $\left ( -1, -175 \right )$, $\left ( -5, -35 \right )$ and $\left ( -7, -25 \right )$

## Prime Factors of $175$

First, note that prime numbers are all positive integers that can only be evenly divided by $1$ and itself. Prime Factors of $175$ are all the prime numbers that, when multiplied together, equal $175$.

All the prime numbers used to divide in the Prime Factor Tree are the Prime Factors of $175$. Here are the maths to illustrate:

$175 \div 5 = 35$

$35 \div 5 = 7$

$7 \div 7 = 1$

Again, all the prime numbers you used to divide above are the Prime Factors of $175$. Thus, the Prime Factors of $175$ are $5, 7$.

## Solved Examples

Example 1: What are the possible factors of $175$?

Solution: The natural numbers that can divide a number evenly are factors of $175$. As a result, the factors of the $175$ are $1, 5, 7, 25, 35 and 175$. If we divide $1755$ by any negative of these integers, then the resulting number will always be a factor of 175. Generally, we consider only positive numbers as factors.

Example 2: Can you assist Aman with adding up all the factors of $175$?

Solution: First, we must take out the factors of $175$.

$175 = 1, 5, 7, 25, 35, 175$

Here we can see the $1755$ are $1, 5, 7, 25, 35 and 175$.

We can conclude here that If you add up all the components of $175$,

you get $1 + 5 + 7 + 25 + 35 + 175 = 248$

Example 3: Is $25$ a factor of $175$?

Solution: Yes, $25$ is a factor of $175$. If $175$ is divisible by $25$, it leaves a quotient of $7$ and remainders $0$. Hence, $25$ is a factor of $175$.

## Conclusion

The number $175$ is odd and composite in mathematics. The only numbers with more than two elements are composite. Each factor is either less than or equal to the original number. A given integer has a finite number of factors. Factors of $175$ are numbers that leave no residue when divided by $1, 5, 7, 25, 35 and 175$.

## FAQs on The Factor of 175

1. Find the first ten multiples of $175$.

We can write as,

$175 \times 1 = 175$

$175 \times 2 = 350$

$175 \times 3 = 525$

$175 \times 4 = 700$

$175 \times 5 = 875$

$175 \times 6 = 1050$

$175 \times 7 = 1225$

$175 \times 8 = 1400$

$175 \times 9 = 1575$

$175 \times 10 = 1750$

Hence, $175, 250, 525, 700, 875, 1050, 1225, 1400, 1575$ and $1750$ are the first ten multiples of $175$.

2. Is the number $175$ a perfect square?

We know that a number that may be written as the product of two equal integers is referred to as a perfect square. Knowing that $175 = 5 \times 5 \times 7$. We can see that the square root of 175 cannot be obtained using prime factorization. So $175$ is not a perfect square.

3. What are the common factors of $5$ and $175$?

A whole number of a factor of two or more numbers is a common factor. To determine the common factors of $5$ and $175$, follow the steps below:

Step 1: List the factors of each integer that is given.

$1$, and $5$ make up the number $5$.

$1, 5, 7, 25, 35$ and 175 make up the number $175$.

Step 2: Identify the shared factors among the given numbers and list them.

1 and 5 are hence the common factors.