2 x 3 x 7
The prime factorization of a number is the set of prime numbers that can be multiplied together to produce that number.
In other words, it is the simplest form of the number. Let’s take a look at how to find the prime factorization of 42.
What are prime numbers?
A prime number is any number that is only divisible by itself and one. So, the prime factors of 42 are:
The smallest prime number is two.
How to find the prime factors of 42
To find the prime factorization of 42, we can draw a factor tree.
A factor tree is a great way to find the prime factors of any number.
They can be drawn many ways for the same number but always end up with the same prime numbers.
Here is an example of a factor tree for 42.
What are all the factors of 42?
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.
To find all the factors of 42 you can draw a factor rainbow to find factor pairs using the divisibility tests or a calculator.
Start 1 x 42 = 42.
Since 42 is an even number it is divisible by 2.
So the next factor pair is 2 x 21 =42
4 + 2 = 6, which is divisible by 3, so 42 is divisible by 3.
So the next factor pair is 3 x 14 = 42
42 is not divisible by 4.
42 is not divisible by 5 because the last digit is not a 5 or 0.
Since 42 is divisible by 2 & 3, it is also divisible by 6.
So the next factor pair is 6 x 7 = 42.
There are no more whole numbers between 6 & 7, so there are no more factors of 42.
This is how the factor rainbow would look for 42.
What are the factor pairs of 42?
1 x 42 = 42
2 x 21= 42
3 x 14 = 42
6 x 7 = 42
Therefore the factor pairs of 42 are 1 and 42, 2 and 21, 3 and 14, and 6 and 7.
What is the Product of Prime Factors of 42?
We can write 42 as a product of its prime factors.
Since the prime factors of 42 are 2, 3, and 7, they multiply together to equal 42.
42 = 2 x 3 x 7
This is how we write 42 as a product of its prime factors.
Negative factors of 42
The negative factors of 42 are -1, -2, -3, -6, -7, -14, -21 & -42.
Both factors need to be negative, or both positive, to result in a product of positive 42
Final Thoughts on finding the Prime Factorization of 42
While we could have easily found the factors of 42 using a calculator or some other online tool, practicing with different methods can help us become better problem solvers. It’s also a fun way to spend an afternoon!
I hope you feel more confident to apply these strategies to not only the prime factorization of 42 but to find the factors of any number. Finding factors is essential to factorize and simplify algebraic expressions so it is an important math skill to master for future topics.