Question

9)Lareina understands factors. Sometimes she has trouble finding all of the factors of a number. What advice would u give Lareina to help her find all of the factors of a number? Demonstrate by finding all of the factors of 110.
10) a. Find two numbers that have 2,3,and 5 as factors. What other factors do the two numbers have in common?

b. Find three numbers that have 2,4,and 8 as factors. What do these numbers have in common?

Answer 1

9. It is a very good idea to divide by the smallest numbers.

First divide by 2 as many times as you can, then by 3, and so on:

110=2*55 (2 is an obvious factor, since the number ends with 0)

2*55=2*5*11 (5 is an obvious factor since the number ends with 5)


10.a

to find a number with factors 2, 3, 5, just multiply these numbers with any other number you want.

number 1: 2*3*5*4=120
number 2: 2*3*5*9=270

The greatest common factor of these 2 numbers is 2*3*5

any combination of these numbers is a common factor to number 1 and number 2, 

so these numbers have in common the factors: 

2*3=6, 3*5=15, 2*5=10, 2*3*5=30 

that is {6, 10, 15, 30}

b.

a number with 8 as a factor, has also 2 and 4 as factors.

so a number with factors 2, 4 and 8 can be found by simply multiplying 8 by any number.

number 1: 8*5=40

number 2: 8*11=88

number 3: 8*500=4,000

these numbers have in common that they all are multiples of 8 (their greatest common divisor is 8)