Factors of 225 Using Prime Factorization
Factors of 225
Factors | Factor Pairs | Prime factorization |
|---|---|---|
1, 3, 5, 9, 15, 25, 45, 75, and 225 | (1,225), (3,75), (5,45), (9,25), (15,15) | 225 = 3 × 3 × 5 × 5 |
What are the Factors of 225?
The factors of 225 are natural numbers that divide 225 without leaving any remainder, or in other words, the factors of 225 divide 225 evenly.
Example: 45 is a factor of 225 because when we divide 225 by 45, it gives us 5 as the quotient and 0 as the remainder.
When a number is divided by its factor then the quotient obtained is also a factor of that number. So here, the quotient 5 is also a factor of 225.
So, to check if any number is a factor of 225 or not, divide 225 by that number and verify whether the remainder is zero or not.
Factor List of 225
The factors of 225 can be obtained by applying the divisibility rules and division facts.
We can stop checking after 15 as the factor pairs start to repeat.
So the factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.
Prime Factors of 225
A factor tree can be used to learn about the prime factorization and prime factors of 225.
From the factor tree, we can see that the prime factorization of 225 is 3 × 3 × 5 × 5 = \(3^2 \times 5^2\).
This means 3 and 5 are the prime factors of 225.
Factor Pairs of 225
Positive Factor Pairs of 225
The factor pair of 225 is the combination of two factors of 225, which when multiplied together, result in 225.
Example: (3, 75) is a factor pair of 225 as 3 x 75 = 225
A factor pair can be a positive pair or a negative pair.
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Rapid Recall
Solved Factors of 225 Examples
Example 1: Find the common factors of 225 and 100.
Solution:
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, and 225.
So, the common factors of 225 and 100 are 1, 5, and 25.
Example 2: What is the greatest common factor of 225 and 250?.
Solution:
Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, and 225.
Factors of 250: 1, 2, 5, 10, 25, 50, 125, and 250.
So the common factors of 225 and 250 are 1, 5 and 25.
Therefore the greatest common factor of 225 and 250 is 25.
Example 3: A soccer volunteer has 225 bottles of water. He wants to arrange these bottles in a rectangular array. How many different arrays can he make?
Solution:
To find the number of arrays that can be made we need the number of factor pairs of 225.
225 has 5 factor pairs, that is, (1, 225), (3, 75), (5, 45), (9, 25) and (15, 15).
Out of these pairs only the first 4 pairs can be arranged in 2 different ways to make rectangular arrays.
The last pair (15, 15) can make only 1 rectangular array.
So the number of possible rectangular arrays = (2 x 4) + 1
= 8 + 1 = 9
Therefore the volunteer can arrange the bottles in 9 different ways.
When you divide 225 by 7, it will give 1 as a remainder, that is, 7 does not divide 225 evenly. So 7 is not a factor of 225.
Yes, 225 is a composite number as it has more than two factors. It has factors 3, 5, 9, 15, 25, 45, and 75 other than 1 and 225.
Numbers which have only two factors, that is, 1 and the number itself are called prime numbers.
Numbers that are obtained by multiplying 225 by any natural number are known as multiples of 225.