Factors Of 175

We can tell if a number has more than 2 factors just by seeing if a number is a prime number or not. As none of the even numbers except 2 are prime numbers, we can tell that 175 has more than 2 factors. Let us find what the factors are.

Negative factors of 175:  -1, -5, -7, -25, -35 and -175.

Prime factors of 175: The prime factors of 175 are 5 and 7.

Prime factorization of 175: 5×5×7

The sum of factors of 175: 1+5+7+25+35+175= 248.
 

Children use multiple ways to find factors of a number. Let us look at some ways we can use to find the factors of 175.

 

• Multiplication Method

 

• Division Method

 

• Prime Factor and Prime Factorization
   

In the multiplication method, we find pairs of numbers where the product will be 169. In this process, possible steps will be - 

Step 1: Find all those numbers whose product will be 175.

Step 2: These numbers will be called the factors of 175.

Step 3: Students have to write these pairs of numbers for this method.

List of numbers whose product is 175

175×1= 175

35×5= 175

25×7= 175

So the pair of numbers whose product is 175 are (1,175), (5,35)  and (25,7).
 

For the division method, the process of division will go on until the remainder becomes zero.

Step 1: For the division method, always try the smallest number to start with. It is advisable to start dividing the number by 1, then both the number and 1 will be its factors. Example: 175÷1 = 175.

Step 2: Then check with the next number to see whether the number is divided completely without any remainder. Both divisor and quotient are the factors. Example: 175÷5= 35 and so on.
 

Prime factorization is the process where the number will be a product of prime factors or prime numbers.

Prime Factors Of 175:The prime factors of 175 are 5 and 7. We find the prime factors of 175 by two ways.

Prime Factorization: Prime Factorization: Here we will divide the numbers by the smallest prime number. Till we completely divide the given number. For 175, the steps are like this:

175/5= 35

35/5= 7

7/7= 1

As 7 is a prime number, it is only divisible by 7. Hence, The prime factorization of the number 175 is 5×5×7.
 

This is a very easy method because in many ways it’s almost the same as a prime factorization. We will break down huge numbers in this case to get what we call a factor tree.

Step 1: 175 divided by 5 gives us the answer being 35.

Step 2: 35 divided by 5 gives us 7.

Step 4: This we can’t divide further.
 

There are positive and negative factor pairs for a given number. Let us look at these factor pairs.

Positive Factor Pairs: (1,175), (5,35)  and (25,7).

Negative Factor Pairs: (-1,-175), (-5,-35)  and (-25,-7).
 

• Factors: Numbers that divide a given number exactly, without leaving a remainder. Example: Factors of 175 are 1, 5, 7, 25, 35, and 175.

 

• Prime Factorization: The process of expressing a number as a product of its prime factors. Example: The prime factorization of 175 is 5² × 7.

 

• Square Root: The number that, when multiplied by itself, equals the original number. Example: The square root of 175 is approximately 13.23, but is not a factor as it's not a whole number.

 

• Greatest Common Factor (GCF): The largest factor that two numbers share. Example: The GCF of 175 and 100 is 25.