Factors Of 225

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 225 has more than 2 factors. Let us find what the factors are.

Negative factors of 225:  -1, -3, -5, -9, -15, -25, -45, -75, and -225.

Prime factors of 225: The prime factors of 225 are 3 and 5.

Prime factorization of 225: 5×5×3×3.

The sum of factors of 225: 1+3+5+9+15+25+45+75+225= 403
 

Children use multiple ways to find factors of a number. Let us look at some ways we can use to find the factors of 225.

• Multiplication Method

• Division Method

• Prime Factor and Prime Factorization
   

In the multiplication method, we find pairs of numbers where the product will be 225. In this process, possible steps will be - 

Step 1: Find all those numbers whose product will be 225.

Step 2: These numbers will be called the factors of 225.

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

List of numbers whose product is 225

225×1= 225

75×3= 225

45×5= 225

25×9= 225

15×15= 225

So the pair of numbers whose product is 225 are (1,225), (3,75), (5,45), (9,25)  and (15,15).
 

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: 225÷1 = 225.

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: 225÷5= 45 and so on.

Prime Factors Of 225: The prime factors of 225 are 5 and 7. We find the prime factors of 225 by two ways

Prime Factorization

Factor Tree

Prime Factorization: Here we will divide the numbers by the smallest prime number. Till we completely divide the given number. For 225, the steps are like this:

225/5= 45

45/5= 9

9/3= 3

3/3= 1

As 3 is a prime number, it is only divisible by 3. Hence, The prime factorization of the number 225 is 5×5×3×3.
 

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: 225 divided by 5 gives us the answer being 45.

Step 2: 45 divided by 5 gives us 9.

Step 3: 9 divided by 3 gives us 3.

Step 4: 3 divided by 3 gives us 1.

Step 5: This can’t be divided any further.

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

Positive Factor Pairs: (1,225), (3,75), (5,45), (9,25)  and (15,15).

Negative Factor Pairs: (-1,-225), (-3,-75), (-5,-45), (-9,-25)  and (-15,-15).
 

• Prime Numbers: Numbers greater than 1 that have no positive divisors other than 1 and themselves. For example, 2, 3, 5, 7.

• Square Root: A value that, when multiplied by itself, gives the original number. For example, the square root of 225 is ±15.

• Sum of Factors: The total obtained by adding all the factors of a number. For 225, the sum of its factors is 403.

• Remainder: The amount left over after division when one number does not divide the other evenly.