Question

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

Answer 1

First Xiao should find the GCF of both (60, 90)

Mistake Xiao made: 60 + 90 = 3( 20 + 3 ) =====> 60 + 90 = 30 (2 + 3

GCF:

60, 90 ======> 30 ========> NOT 3

Answer:

GCF = 30

For the values 60, 90

Solution by Factorization:

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Then the greatest common factor is 30.

GCF * 60, 90 ====> 60 * 90 / LCM (60, 90 )

5400 / 180 ========> 30

The correct answer:

60 + 90 ========> 30 * 2 + 3

Therefore, the mistake Xiao, made was writing a 3 instead of writing 30.

Hope that helps!!!!!! : )

Answer 2

The greatest common factor is at least 10. That comes from the two zeros, one on 60 and the other on 90.

10(6 + 9) Now you can take out 3 more 10*3 (2 + 3) = 30 * (2 + 3). There is another more mathematical way to do this. Factor using prime factors.

60 = 2 * 2 *3 * 5

90 = 2 * 3 * 3 * 5

Put all the bolds together. 2 * 3 * 5 These numbers represent the highest common factor.

GCF = 2*3*5 = 30