PRODUCT OF PRIME
FACTORS
Product of Prime Factors
ANY whole number can be broken down and
written as a Product of Prime Factors
What is a PRIME FACTOR ?
A PRIME FACTOR is a FACTOR that is also a
PRIME NUMBER. Lets do a factor example ...
The Prime Factors of a Number
Example Question
Express 108 as a Product of Prime Factors
We use the “Factor Tree” Method
108
12
4
2
3
2
9
3
3
Prime Factors are the
“fruits” of our “tree” .....
Product of Prime Factors
....from the previous page we obtained
2, 2, 3, 3, 3 as PRIME FACTORS of 108
So 108 = 2x2x3x3x3
108 = 22 x 33
Product Of Prime Factor Questions
1) Express 240 as a Product of Prime Factors
2) Express 150 as a Product of Prime Factors
3) Express 256 as a Product of Prime Factors
4) What do you think Highest Common Factor
and Lowest Common Multiple mean ?
Product of Prime Factors Answers
1) Express 240 as a Product of Prime Factors
2x2x2x2x3x5 = 24 x 3 x 5
2) Express 150 as a Product of Prime Factors
2x3x5x5 = 2 x 3 x 52
3) Express 256 as a Product of Prime Factors
28
4) What do you think Highest Common Factor
and Lowest Common Multiple mean ? .......
HCF
Highest Common Factor (HCF) is the biggest
number that will divide into both of two or all
of more numbers ...
The HCF of 240 (2x2x2x2x3x5) and 150
(2x3x5x5) is 2x3x5 ..... Why ?
Because 2x3x5 are the numbers in both lists,
So HCF of 240 and 150 = 30
HCF Questions
The following numbers have already been
broken down into Products of Prime Factors,
find the Highest Common Factors ...
1) 2x2x2x3x3x5 and 2x3x3x5x7
2) 3x3x3x5x7x7 and 2x2x3x3x7x11
3) 5x5x7x11x11 and 2x5x7x11x13
HCF Answers
The following numbers have already been
broken down into Products of Prime Factors,
find the Highest Common Factors ...
1) 2x2x2x3x3x5 and 2x3x3x5x7
2x3x3x5
1) 3x3x3x5x7x7 and 2x2x3x3x7x11
3x3x7
1) 5x5x7x11x11 and 2x5x7x11x13
5x7x11
LCM
Lowest Common Multiple (LCM) is the lowest
number that both numbers are FACTORS of ..
1) Find the LCM of i) 2x2x3x5 and ii) 2x5x7
Do the minimum possible to make both
products the same ..
i) 2x2x3x5x7
ii) 2x5x7x2x3
LCM = 420
LCM Questions
Find the Lowest Common Multiples ...
1) 2x3x5x7 and 2x2x7
2) 2x3x3x5x7 and 3x11
3) 2x2x2x13 and 3x11x13
4) 2x7 and 3x19
LCM Answers
Find the Lowest Common Multiples ...
1) 2x3x5x7 and 2x2x7
2x3x5x7x2
2) 2x3x3x5x7 and 3x11
2x3x3x5x7x11
3) 2x2x2x13 and 3x11x13
2x2x2x13x3x11
4) 2x7 and 3x19
2x7x3x19
Summary
• Any whole number can be broken down into a
Product of Prime Factors.
• We use the “Factor Tree” method where the
Prime Factors are our “fruit”.
• Products of Prime Factors can be used to find
Highest Common Factors and Lowest Common
Multiples.