Posted by **Hailey 6th grade** on Thursday, August 28, 2014 at 7:43pm.

1.Tasha believes that she can rewrite the difference 120-36 as a product of the GCF of the two numbers and another difference.Is she correct?Explain your answer.

2.Explain how to find the GCF of three numbers

3.Xiao's teacher asked him to rewrite the sum 60+90 as the product of the GCF of the two numbers and a sum. Xiao wrote 3(20+30). What mistakes did Xiao make? How should he have written the sum?

- Advanced Math -
**Steve**, Thursday, August 28, 2014 at 8:14pm
yes.

As long as the GCF is not 1, then since the GCF divides both numbers, it divides their difference.

For three numbers, extend the method as for two. Fins all the prime factors and their powers, and pick the highest power of each prime that appears in all three lists.

3 is not GCF(60,90)

- Advanced Math -
**Reiny**, Thursday, August 28, 2014 at 8:25pm
1.

Written in more "mathematically friendly language"

Factor fully:

120 - 36

= 12(10 - 3)

2.

- express each number in factored form

- Your GCF consists of the products of all the factors found in ALL three numbers

e.g. 60 , 84, and 150

60 = 2x2x3x5

84 = 2x2x3x7

150 = 2x3x5x5

GCF or HCF = 2x3 = 6

3.

See # 1.

Xiao's teacher is only confusing his/her students by this strange wording,

How about just asking to "factor fully"

60+90

= 30(2 + 3)

btw, Xiao did not make a mistake, she simply did not complete her solution.

What she had so far is correct.

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