What you need to know
Things to remember:
- Learning the prime numbers less than 30 is always helpful.
- A prime factor decomposition is all of the prime numbers multiplied together that make the number.
- If you can divide by a prime number to start with, it will make the process quicker.
- Number that end in a 0 can always be divided by 10.
A factor is a number that divides another number and gives a whole number. For example, because 32\div8=4, then 8 is a factor of 32. This means that 4 is a factor of 32 as well. We call these two numbers, 4 and 8, a factor pair. We can also think of the factor pairs as multiplying:
Factors of 32:
1 2 4 8 16 32
A prime factor decomposition is all of the prime numbers that multiply together to make the original number. So, to find a prime factor decomposition, it is helpful to know your prime numbers.
Find the prime factor decomposition of 420
We can find a prime factor decomposition in two.
Method 1: Prime Factor Tree
We can do this in four steps:
Step 1: Start by writing your number at the top middle of the page.
Step 2: Think about two numbers that multiply together to make your number, writing these down to the sides, connecting with straight lines, and circling any prime numbers.
Tip: Try to divide by a prime number to start with, as this will speed up the process!
Tip: If your number is even, you can divide by 2, which is prime.
Step 3: Repeat Step 2 on the numbers that haven’t been circled until the ends of each branch are circled.
Step 4: Write all of the prime (circled) numbers together as a multiplication.
Tip: You can write this the multiplication with powers.
Method 2: Multiplying through.
Instead of drawing out the prime factor tree, you can write it as a multiplication, breaking up number into factors until you are left with prime numbers.
Question 1: Find the prime factor decomposition of 212
Question 2: Find the prime factor decomposition of 400
400=2\times 2\times 100
400=2\times 2\times 10\times 10
400=2\times 2\times 2\times 5\times 10
400=2\times 2\times 2\times 5\times 2\times 5 =2^4\times5^2
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