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