To find the prime factors of 100 first you need to find the factors of 100, then identify which factors are prime numbers.
This article will show you how to apply these 2 skills to this problem.
As a high school mathematics teacher for over 14 years, I have noticed that my students who have mastered these skills are able to easily apply them to other topics such as Algebra and Fractions where knowledge of factoring is essential.
What are the factors of 100?
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100.
Factors are numbers that divide into a whole number evenly with any remainder.
What is the prime factorization of 100?
To find the prime factorization of 100 first you need to draw a factor tree.
The factors circled in red are prime numbers.
Prime factorization of 100 is the process of finding which prime numbers multiply together to equal 100.
So we can see that 100 = 2 x 2 x 5 x 5
How to find the prime factors of 100.
After identifying the factors of 100; 1, 2, 4, 5, 10, 20, 25, 50 and 100, which of these factors are prime numbers?
The prime factors of 100 are 2 & 5.
What are the Factor pairs of 100?
To find the factor pairs of 100 I like to draw a factor rainbow.
Watch me draw a factor rainbow for 90 here.
The factor pairs can be written as a product like this:
1 x 100 = 100
2 x 50 = 100
4 x 25 = 100
5 x 20 = 100
10 x 10 = 100
There are 5 factor pairs of 100.
What is the product of prime factors of 100?
The product of prime factors of 100 is:
100 = 2 x 2 x 5 x 5
The can be written in index notation like this:
Negative factors of 100
Two negative factors multiply together to equal a positive number.
-1 x -100 = 100
-2 x -50 = 100
-4 x -25 = 100
-5 x -20 = 100
-10 x -10 = 100
Both factors must be negative (or both positive) to result in a product of positive 100.
Example problem 1
Find the common factors of 100 and 90.
Solution:
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50 and 100.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
The common factors of 100 and 90 are 1, 2 & 5.
Example problem 2
Find the average of the factors of 100
Solution:
Average = sum of the factors/ number of factors
= (1+2+ 4+ 5+ 10+ 20+ 25+ 50 + 100)/9
= 217/9
=24.1
FAQs
What is the sum of the prime factors of 100?
The prime factors of 100 are 2 and 5 so the sum is 7.
Conclusion
By understanding what factors are, and how to find them, you can open up a whole new world of mathematics! 100 is a great number to start with because it has so many different factor pairs.
If you want to get really good at finding factors, try picking a random number and seeing how many different ways you can break it down. You might be surprised at how many there are!
Keep practicing, and before you know it, finding prime factorizations will be a breeze.
Further factors
Learn more about the factors of other numbers here.
