Page 19 - Math Smart - 7

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Write the number of Write the number 16
24 as the product of its as the product of its
Draw the factor tree Repeat the process for the
prime numbers. prime numbers.
for number 24. other number, that is 16.
24 = 2X2X2X3 16 = 2 X 2 X 2 X 2
= 23 X 3 = 2"

The HCF of 24 and 16 is the product of the prime factors
that are common to both numbers. 24 = 2X2X2X3
16 = 2 X 2 X 2 X 2
The numbers 24 and 16 both have a prime factor of 2.
There are three prime factors of 2 in the number 24.
There are four prime factors of 2 in the number 16.
Therefore, only 2 x2 x2 is common to both 16 and 24.

h
2X2X2=8
Chris can make 8 arrangements with the
same number of each flower colour.
Each arrangement will have
24 T 8 = 3 orange flowers and
16^8 = 2 yellow flowers.

Check My

Understanding

o Use factor trees to find the HCF of the following numbers.
a) 15 and 30 b) 12 and 16 c) 15 and 20 d) 28 and 96 e) 10, 16 and 40
e Josh is making identical balloon arrangements for a party. He has 32 red balloons, 24 white
balloons, and 16 orange balloons. He wants each arrangement to have the same number of
each balloon colour. Use a factor tree to find the greatest number of arrangements that he
can make if every balloon is used.

e