# Prime Factor Form

There are many ways to introduce and express numbers as a product of prime factors but recently I have been looking at questions that use prime factor form.

I’m not including HCF or LCM in this because most teachers have used PFF to solve HCF and LCM problems before.

Here are some questions I have written that can be solved easily using PFF

These are on the ppt below

Prime Factor Form

I also like this activity I made, its simple practice but saves paper if you display it as a ppt

Update

I made this starter to use with year 10

Prime Factor Form Questions

UPDATE! Prime Factor Form Challenge. The idea is students are faced with increasingly more challenging PFF questions. They need to think about divisibility to help them and they know the numbers are listed below. It can generate some interesting discussions about numbers/divisibility. Students who are faced with a large number that isn’t divisible by 2, 3 or 5 may believe the remainder is a prime number. Once the number is written in PFF they can asign the correct letters and unscramble the word.

Here is the ppt for PFF pff

I was thinking about the factors particular numbers and considered how many factors int he numbers from 1-40. When I reached the 30s I was surprised how many numbers could be written as a product of two primes, meaning they have 4 factors in total. So I started wondering about what students would make of it. Would they realise if the number was written as a product of two primes it would have 4 factors and would they realise you could easily find a number with 4 factors by multiplying 2 primes together.

33=3×11

34=2×17

35=5×7

38=2×19

39=3×13

# Prime Numbers and Factors

The link for the ppt for the puzzles below

There are so many great resources for students to look at factors and primes. Depending on set and age, I have used many varied problems and questions. Sometimes I start with Squares, Sticks or Rectangles. For this task students take 1 square and they have to arrange it as a square, if this isn’t possible they try a rectangle with length greater than one, if this isn’t possible they draw a stick (one dimension can be 1). So they draw a square for 1, sticks for 2 and 3, then a square for 4, stick for 5, a 3×2 rectangle for 6, a stick for 7 and so on.

Another way I like to start this topic is with this question

Students start discussions of divisibility and more often than not students mention primes. This question is also nice when looking at sequences. Students think about generating a list of possible numbers and it starts conversations about which numbers can be used ‘it will be odd as cant divide 2 exactly’

Once students are familiar with the terms ‘factors’ and ‘prime’ I like to move one to some problems where it tests their abilities to determine whether a number is a prime or what factors it has.

I usually use the above task as a plenary task which you’ll find on the ppt below and I sometimes restrict the numbers and other times allow them to use any number.

Types of Number

The two task above are from the worksheet below and students have to think about factors of numbers but it also introduces HCF and finding common factors of two numbers.

Factor 2 Way Tables

I usually finish with a task like below and although you get the students picking out 20 because its the only EVEN you do get students using ‘factor of’ and ‘not a prime’

It leads to some interesting discussions.

This proved an interesting starter. Some students filled it in then realised it didnt add up to 15!

Updated for Christmas!

A simple dot to dot snowflake for students to do as a starter