Prime Factor Tree

Discovering Prime Factors

of Any Number

Definitions

Prime Number – An integer whose only factors are 1 and itself.

Factor – a number that can divide another number without a remainder.

Prime Factors – an expression of numbers that divides another integer without a remainder where all the factors are prime.

Let’s Choose a Number

Let’s use 36 Choose any 2 factors

– let’s use 9 and 4 Now let’s factor these

numbers, too Next, arrange them

from least to greatest Last, re-write as

exponents

36

49 x

2 2 xx 3 3

22 x 32

2233 xx

Let’s Try That Again!

Let’s use 36 again Choose any 2 factors – let’s

use 3 and 12 Now let’s factor these

numbers, too Oops, 6 is not prime - let’s

factor again! Next, arrange them from least

to greatest Last, re-write as exponents Look, it’s the same answer!

36

3 xx 26

123 x

3 xx 32 2x

2 x 3x x2 3

22 x 32

Let’s Re-Cap

Composite numbers are made up of factors

In a Prime Factor Tree, the goal is to keep reducing each factor to its lowest possible prime factors

When you have all the prime factors identified, re-arrange them from least to greatest and re-write them as exponents

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